The Assembly or PutTogether class includes those puzzles which entail the arrangement of
pieces to make specific shapes in either two or three dimensions, to mesh in a particular way (without necessarily interlocking) or to fill a container or tray.
The pieces are free to be juxtaposed in many different configurations but only one or a few arrangements will be valid solutions. The best such puzzles often permit a seemingly valid construction of all but one of the pieces, where the last piece stubbornly just won't fit!
For the most part, the order in which the pieces are put together does not matter  when order does matter, it is a sequential assembly puzzle.
If the pieces truly interlock to form a freestanding construction that remains stable in various orientations, the puzzle belongs in the Interlocking class. If the pieces have designs on them and there are rules about how the designs must appear, check the Pattern class or the Jigsaws class.
Simply stated, the challenge of a packing puzzle is to fit a given set of pieces into a container. The boundaries are either enforced by walls and a lid, or sometimes just walls, with the "lid" implied by the requirement that no piece extends beyond the level of the walls. The container might also be more of a tray, especially if the pieces don't stack in 3 dimensions.
Now, if you consider this task in the abstract, the entire container could be construed as implied rather than physical, and then many assembly puzzles could be considered to be packing puzzles. For example, the SOMA cube could be recast as "fit the pieces into a cubic box." In addition, you can shoehorn dissections in here by thinking of the original form as the "container"  the objective is to reconstruct the original form, which is tantamount to fitting the pieces back into this abstract container.
For my purposes here, I will include a puzzle in the "packing" category if there is a physical container, and some pieces to cram into it. In rare instances the container is similar to the pieces themselves. Sometimes the puzzle is presented with a subset of all the pieces except for one of them packed into the container, with seemingly no room for the additional piece, and the objective being to rearrange the pieces to make the last piece fit, too.
Take a look at Erich Friedman's Packing Center.
Bill Cutler has written an interesting essay on box packing puzzles.
In addition to his seminal designs of Interlocking puzzles, Stewart Coffin has designed many great packing puzzles. When Coffin's designs appear in the tables below, I have highlighted them like this.
Hercules  B&P Designed by Jean Claude Constantin Nice quality and poses just the right amount of challenge. 
Crazy L A very nice little packing challenge, from the Puzzle and Craft Factory. 
Four T's  Binary Arts/Thinkfun 
Pack the Tray (8 triangles + 1 rectangle)  Saul Bobroff I got this prototype from Saul at the 2009 NYPP. 
Houses and Factories Designed by Richard Hess  distributed by B & P 
Foxes and Wolves Designed by Richard Hess. Purchased at IPP 29 in SF. 

Lucky 7  Melissa & Doug 
Blockade  B&P Blockade is like Lucky 7  both use 3 small and 4 large L shaped pieces, but Blockade also has pins on the board and corresponding holes in the pieces. Lucky 7 is trivial to solve  Blockade adds a little (but not much) challenge. 
Butterfly  Nature's Spaces Fit nine identical pentahexes into a triangular frame. Only one arrangement will work. 
Frog Pond  Nature's Spaces Fit nine identical tetrahexes into a triangular frame. 
3 Ls Fit the 3 Lshaped pieces into the tray. 
Snake Pool Eleven cubes are loosely strung along an elastic to form a cube snake. Fit the snake flat in the tray  the "pool." There are at least four different solutions. The cubes are 3/4", the tray opening is 3.25" square. The snake configuration is: 3+2+2+2+1+1 (where a + denotes a rightangled bend that can swivel). Erich Friedman shows various squareinsquare packings on his Packing Center site, but I don't think the solution shown for 11 squares works with this particular cube snake configuration. 
Packing Quarters  B&P 
Kinato Kinato is a very nicely packaged puzzle from Ravensburger. Sixteen triangles are threaded via clever swivel connections. Arrange them into a large triangle with the proper pattern. I found it at jigsawjungle.com. 
Ampelmann  Roman Götter and Peter Knoppers Purchased from Roman at IPP31 in Berlin A black case with a hidden complex interior and two circular openings. Three red "Don't Walk" Ampelmann figures, and three green "Walk" figures (one mirror image or the other two), colored on only one side. Two challenges: 1) place all six figures in one "compartment" with one red Ampelmann in the middle, and 2) place all six figures in the other "compartment" with one green Ampelmann in the middle. The clear piece is a hint  it shows the shape of the cavity inside the case. Simple, eh? These figures are the old East Berlin crosswalk signal symbols  one of the few vestiges of Communist rule that Berlin citizens want to keep. Read more about " Speciation and Competition in Berlin's Traffic Lights." 
Mimi packing puzzles: A, F, H 

Modest Hexominoes by Dr. Richard Hess (IPP17) Place all 20 pieces so that each hexomino shape contains five identical pieces. Includes a booklet with 100 additional problems to maximally cover polyomino shapes with congruent tiles. 
The Massai packing puzzle from Siebenstein Spiele, 2011. Pack the 5 identical Lshaped tetrominoes in the tray. My copy might be defective, but I found one solution and my wife and kids found two more. 

Quartet in F  Stewart Coffin (#253) 
Octet in F, designed and made by Stewart Coffin, exchanged at IPP32 by Rosemary Howbrigg 
FN Puzzle  pack the four pieces in the tray in three different ways designed by Mitsuhiro Odawara produced by Toshiyuki Kotani Purchased at IPP32 
Retrofit  designed by Goh Pit Khiam, made by Eric Fuller, from Rosewood, Ipe, Walnut, Bubinga, Padauk, Maple, and Acrylic. 
The following traypacking puzzles were all designed by
Edi Nagata.
Edi sells versions in 2sided trays, made from MDF. A couple were offered by Bits and Pieces with wooden 2sided trays and aluminum pieces, other singlesided versions in CD cases by Embrain via Torito. 

Pencil Case 
Shirt Case Purchase the 2sided MDF version from Edi, or the singlesided CDcase versions "Shikoku" and "Australia" from Torito. Philos offers a version, too. 

Arrow Case aka Packing Arrows  B&P 
Cat Case aka Cats in a Cradle  B&P 
Cup Case 
Baby Ducks Case 
This is a special group where the pieces aren't identical, but they are related by some rule or theme, which distinguishes them from those puzzles in the more generic group having an assortment of dissimilar pieces. Some of the puzzles in the latter group may languish there though they belong in this section because I am unaware of the rule relating the pieces...
One event at the International Puzzle Party (IPP) is called the Edward Hordern Puzzle Exchange.
Qualifying attendees can sign up to participate  each must submit a new puzzle design,
and if approved, bring enough copies of the puzzle to exchange one with each other participant (up to 100).
IPP32 in Washington D.C. in 2012 was the first time I participated in the exchange.
There were 79 puzzles in the exchange in 2012.
For the exchange, I created a traypacking puzzle I call NonConvex BiHalfHexes. Catchy and mellifluous, eh? I chose to use a subset of the hexiamonds as pieces. If one divides a regular hexagon in half along a line connecting opposite vertices, then rejoins the two halves along a sidelength, there are only seven resulting shapes that are nonconvex. Using the "standard" piece names, this set of seven includes { butterfly, chevron, crook, hook, snake, sphinx, yacht }. The other five hexiamonds are either convex { rhomboid, hexagon }, or not composed of two halfhexes { crown, pistol, lobster }. I used this set of seven (mathematically complete given the defining rule) and designed four different simple symmetric trays into which all seven pieces can be packed flat (allowing gaps), three of which have only one solution apiece. The puzzle was produced by Steve Kelsey at AccurateLaserEngraving.com. The case cover is made from a single piece of wood, with a clever lasercut flexible "binding." We designed a nice dovetail closure. From what folks tell me, this is a difficult puzzle. If you are interested in purchasing a copy, please email me at the address on my home page.


I have been working with Steve Kelsey to design an expansion set for my IPP32 exchange puzzle NonConvex BiHalfHexes. I have come up with a dozen new tray shapes into which all seven pieces will fit flat. Difficulty ranges from easy to hard, with several having only 1 or 2 solutions, but a few having 7, 9, and 12 solutions. All of the trays are "hollow" and require no internal islands. Our intent is to make the original puzzle and the expansion set available for purchase via Steve's Accurate Laser Engraving website. Stay tuned!


Nine Squared  Tom Lensch All nine pieces have identical thickness but each has a different combination of length and width selected from discrete increments within a narrow range. When arranged correctly into the tray they simply drop in and out with no binding. Several incorrect packings seem like they should fit, if only you press down a little... wrong! 
Apothecary's Cabinet  Constantin (purchased at GPP) Each "drawer" has a combination of side tabs and portions of the row separators, and is equivalent to a rectangle with each side having either a tab or a notch. There are 2^4=16 possible arrangements including rotations and reflections. The knobs on the drawers require the reflections. The fact that the side tabs/notches are offcenter requires the rotations. This puzzle is a nice realization of a 4x4 heads/tails edgematching puzzle, but includes a cabinet/tray/frame which constrains the solution, since it has all notches along the left and top, and all tabs along the right and bottom. If you assign a 4bit binary ID to each drawer using 0 for a notch and 1 for a tab, the low bit for the top and high for the left side, then one solution is:
For issues 61 and 62 (Nov 2003) of the CFF newsletter, Dieter Gebhardt wrote articles analyzing this puzzle, and in issue 62 reports results derived by Jacques Haubrich. 

Digits  Constantin Fit the 10 digits into the tray. 
Partridge Puzzle by Robert Wainwright obtained from Robert at the 2007 NYPP Kadon offers some of Erich Friedman's "Partridge" puzzles. In an "antiPartridge" puzzle, there is one largest piece, and the count goes up as the pieces shrink. 

Square Dance  designed by Derrick Schneider Purchased from Pavel Curtis  I've been wanting one for a while and was pleased to find Pavel had resuscitated it! Square Dance won an Honorable Mention in the 2002 IPP Design Competition. There is only one way to join two 2x2 squares by a half edge, and only four ways to join a third 2x2 square by a half edge to the first two. These are the four pieces of Square Dance, and there is only one way to pack them into an 8x8 tray, and only one way to pack them into a 7x9 rectangle. The included tray is twosided. 
Lonpos Cosmic Creatures 

The muchcopied Digigrams, designed by Martin Watson. Made by Eric Fuller, from Grandillo, Walnut, and lasercut acrylic. 
Pentagon Tiles, designed and exchanged at IPP32 by Rene Dawir, made by Marcel Gillen 

13 Triangles, designed and exchanged at IPP32 by Ed Pegg Jr., made by William Waite 
DiHalfHexes, designed and exchanged at IPP32 by Peter Knoppers, made by Buttonius Puzzles & Plastics I was really surprised to see this one, since it is so similar to my NonConvex BiHalfHexes IPP32 exchange puzzle. What are the odds? Peter and I must have been hit by a similar brain wave. Fortunately, his puzzle uses a different set of hexiamonds and different trays. 

Triangle Edges  designed by William Waite in 2005 Pack the 12 pieces into the tray. The puzzle is based on a triangular grid and each piece is composed of five edges. 
Karin's Star Cluster An entry in the IPP24 Design Competition. 
Tessellating Galaxies  JVK 
Sun Dance  JVK 
The City 2001 Binary Arts (Thinkfun) Pack six heptominoes (3 distinct pieces and their mirror images) in the 6x7 tray. Nice metal pieces with 3D abstract buildings on them which prevent the pieces from being flipped and exclude most of the otherwise possible 80 assemblies. 

Geometrex Set  Ormazd, Nabucho, and Quirinus In each case the pieces can be rearranged within the tray to fit in an extra square. 
Fit To A Tee  Thinkfun A nice metal traypacking puzzle from Thinkfun. Pack the 9 pieces representing golf holes complete with tees, sand traps, and pins, into the base. The base presents a challenge on each side (the front and back nines), with different arrangements of fixed water hazards to work around. Oh, and just as on a real course, abut each flag with the tee of the next hole! 
Fantastic Island 
The IQ Link puzzle from Smart Games designed by Raf Peeters 

The "845 Combinations" puzzle is almost like pentominos... here is a solution to the 845 puzzle. 
On 6/2225/13, made a trip to Niagara Falls. At Niagara Falls, I stopped in at Turtle Pond Toys. They carry several nice puzzles of various types. I picked up the IQ Puzzle from Toyland Company. It has 9 curved pieces that must be fit into the channels within a 4x4 grid of circles. It is an easier version of the 845 Combinations puzzle, which has 10 pieces to be fit into the same grid. 

Adam's Cube 
One Way 
Boxed In  Milton Bradley 
Circle Challenge  Melissa & Doug A good one for kids  work on it from the inside out. The pictures on the pieces are merely decorative. 

Magic Block (MCS promo) 
Figa Block 
IQ Block 
Double Cross  Mag Nif There are four pink plastic pieces and the tray. The objective is to form a cross (plus sign) in the tray. 

Build the Block  a metal square dissection puzzle branded "Arco." 

Sleazier  Pavel Curtis based on Stewart Coffin's Four Sleazy Pieces (#169A) Fit the 4 polyominoes into the tray. IPP25 
Stewart Coffin's Sunrise / Sunset (#181) Fit the 5 polyominoes into each side of the tray, making a symmetric pattern in each case. Gift from Bernhard Schweitzer (thanks!). IPP22 
Stewart Coffin's Drop In (#153B) aka The Trap Fit the four pieces into the box through a small slot. They must be arranged so all fit within the inside perimeter of the box walls. Saul Bobroff IPP23 
Stewart Coffin's Few Tile (#133) Made by John Devost A beautiful Padauk frame about 5.75" squared, with corner splines, and Birch plywood pieces. A gift  Thanks, John! 

Stewart Coffin's Four Fit (#217) Made by Tom Lensch. Purchased from Tom at the Dartmouth College Mechanical Puzzle Day in Feb. 2008. 
Stewart Coffin's Five Fit From Dave Janelle at Creative Crafthouse. Fit the five pentomino pieces into the square tray. The tray has a handy storage space for one of the pieces should you be unable to solve it. 
A Stewart Coffin Tray Puzzle Set (#181), in Poplar and Lyptus woods, made by Tom Lensch. Purchased at PuzzleParadise.ca. This set includes six of Coffin's traypacking puzzles  a singlesided rectangular tray (#181, 1 solution), a twosided pentagonal tray (#181C, The Housing Project, 1 solution each side), and another twosided pentagonal tray having a movable wall segment on one side (#181A, The Castle Puzzle, 3 solutions; #181B, The Tree Puzzle, 2 solutions, other side #181B, The Vanishing Trunk Puzzle, 1 solution). 
Stewart Coffin House Party (#250) Fit the four Marblewood pieces into each side of the tray, which is made from Poplar on Baltic Birch. Made by Tom Lensch 

Stewart Coffin's Cruiser (#167) Made by Walter Hoppe. 
Lean 2, designed by Stewart Coffin, made by Tom Lensch, exchanged at IPP32 by Dave Rossetti 
Buridan, designed, made, and exchanged at IPP32 by Vladimir Krasnoukhov 
Heart and Bud, designed, made, and exchanged at IPP32 by Yoshiyuki Kotani 



Think Square  Pressman There are 4 small right triangles, 4 large right triangles, 4 staircase shaped pieces, and 5 small squares. The pieces can be fit snugly into the tray with and without one of the five small squares. 
Triadenspass  Logika 
Pack It In  Great American Puzzle Factory 1996 Pack a set of 16 items into a suitcase frame. Flat cardboard pieces. 
The Trapped Man  Tom Jolly Laser cut by Walter Hoppe. Five unusually convoluted pieces, including the little "man." The first challenge is to fit them into the tray so that none can slide or rotate. Next, try it with only four of the five pieces, then with only three! Several other puzzle goals accompany the Trapped Man puzzle. 

PacMan  Milton Bradley First create 4 Pacmen with open mouths. Then use the same pieces to create 3 Pacmen with closed mouths. There are eye stickers on some pieces, which must be positioned correctly. The pieces can be flipped. 
The Jayne Fishing Puzzle  A 1916 advertisement of Jayne's Tonic Vermifuge (yuck!). Discussed in Slocum and Botermans' "The Book of Ingenious and Diabolical Puzzles" on page 15. You were to cut out the fish and the ring and then pack the fish inside the ring. The fish names are (left to right, top down): Codfish, Shad, Red Grouper, Cowtrunk Fish, Flying Fish, Bluefish, Mackerel, Tarpon, Sheepshead, Moonfish, Striped Bass, and Weakfish. Also see No Fishing by Bepuzzled. 
No Fishing  Bepuzzled 1998 Remove the water then fit all twelve fish into the bowl. This is a nice wooden lasercut, colorful, and faithful copy of the Jayne Fishing Puzzle of 1916. 

In the Raging Rapids puzzle from Thinkfun (Binary Arts), you have to fit all the men into the raft, facing the right way. The figures' bases have various patterns of tabs and indents. 
In the Mayan Calendar puzzle from William Waite, you have to fit all the glyphs into the tray, facing the right way. The glyphs have various patterns of tabs and indents. (Similar to Raging Rapids.) 
Alex Randolph's Moebies  Springbok 1973 There are 8 sockets at various positions in the orange board. Six pieces and six pegs are included  the object is to find a way to peg the six pieces to the board so that all fit within the edges. 
Springbok Fitting & Proper 

Here is a nice set of small, pocketsized tray packings designed by William Waite, purchased from his
PuzzleMist website:
From left to right, they are: Triangle Quorn, Square Quorn, Hex Quorn, Diamond Teaser, and Mix Teaser 2. 

The Kitchen Ceiling Puzzle  designed by William Waite in 2006 Pack the 12 pieces into the tray so that the holes make symmetric patterns. 
Optimal Tumble  designed by William Waite in 2010 Pack the 12 pieces into the tray so that the holes make symmetric shapes. 

Vintage 1969 packing puzzles from Lakeside. So far they include:


JVK Tessellating Hexagons 
Galaxies & Stars  JVK 
"Tripple 7"  3piece packing (prototype)  JvK 

Easy Eight / Hard Eight  Bob Hearn 
Wetten Dass... Also known as FACT Purchased in Berlin. The tray has a moving bar, pivoted at one corner. When the bar is aligned along the top edge, the five pieces are easy to pack into the tray. When the bar is aligned along the side edge, it's more difficult. 
Toysmith 11 pc. wood puzzle 
Mind the Gap  Chris Morgan 

Some tray packing puzzles designed by Naoyuki Iwase (Osho) 
Mouse, Tulip, and Seals:
See Osho's website, PuzzleIn. 

eLeL4  designed by Hiroshi Yamamoto presented at IPP30 by Hiroshi Uchinaka Fit the four pieces into the 8x8 tray. Each piece is composed of 2 'L' shapes. 
Unique U  designed by Hiroshi Yamamoto Fit the six Ushaped pieces into the 9x9 tray. 
The Nifty Fifty from Jean Claude Constantin requires you to pack the four pieces into the tray. 
The Quartet Puzzle  the Quartet's tray has a movable end wall, and you must pack specific subsets of pieces into the tray depending on where the wall is positioned. 

Four in a Frame  a twosided fourpiece tray packing puzzle based on a triangular grid, designed by Markus Götz 

PackMan  Chris Enright 
Hexagon 10 
Game Ball Puzzle 

Animals of Australia Dump out the ten nicely cut animal pieces and try to fit them back in the tray. No peeking at the solution! 
Forever Wild  Animals of the Adirondacks Pack the ten nicely lasercut animals into the tray. The animals all go in with a specific side upwards. From Creative Crafthouse. 
Forever Wild  Animals of the Appalachians  a tray packing puzzle, one of a series  each comprising a highquality tray and nice lasercut pieces in various colors. 
The Cook's Cupboard Puzzle Pack the eleven kitchen items into the tray. From Creative Crafthouse. 

Hexus, a packing puzzle from Brainwright. Seven pieces and a movable "challenge block" to be placed on a hexagonal grid according to a series of 44 challenges. Purchased at Necker's. 
Quadrillion  designed by Raf Peeters, produced by SmartGames Thanks, Raf! Arrange the four base plates per a challenge, then pack the pieces on. 
This section describes several types of puzzle in which assortments of square pieces or tiles must be packed in various ways. Much study and analysis has been done in this area, and there are some great resources on the web. Topics include:
The problem of Mrs. Perkins' Quilt (or Mrs. Perkins's Quilt) appeared as no. 173 in
Henry Ernest Dudeney's 1917 book Amusements in Mathematics.
You can find the book and the problem online in a few places, including
at
www.gutenberg.org, and at
www.scribd.com.
The problem: given a large square quilt made of 13x13 small squares (169 small squares total), find the smallest possible number of square portions of which the quilt could be composed  i.e. a dissection of the large square into a number of smaller squares that don't all have to be different. However, only prime dissections are allowed  the side lengths of the component squares cannot all have a common factor  they must be relatively prime. There can be no subsquare which is itself divided  such a solution is termed "primitive"  primitive quilts are quilts without subquilts. Martin Gardner devotes chapter 11 in his 1977 book Mathematical Carnival to Mrs Perkins' Quilt and Other SquarePacking Problems. Ed Pegg discussed the problem on his Math Games site. The problem is also discussed at mathworld.wolfram.com. The solution comprises 11 squares and is shown at gutenberg.org. It contains the following number of squares of given sizes: 1x7^{2}, 2x6^{2}, 1x4^{2}, 2x3^{2}, 3x2^{2}, and 2x1^{2}. The smallest numbers of squares needed to create relatively prime dissections of an n×n quilt for n=1, 2, ... are 1, 4, 6, 7, 8, 9, 9, 10, 10, 11, 11, 11, 11, 12, ... (Sloane's A005670). Karl Scherer discusses additional variations at his website. Karl defines a nowhere neat tiling  in which no two tiles have a full side in common, and a no touch tiling  where tiles of same size cannot touch, noting that notouch are always nowhereneat. 
The problem of Mrs. Perkins' Quilt leads to other questions.
In general, how might it be possible to dissect various rectangles or squares into smaller squares?
Such puzzles are known as Squared Rectangles and Squared Squares.
If a dissection results in pieces all of different sizes, the dissection is called perfect, otherwise it
is imperfect.
If the dissection does not contain any smaller square or rectangle that is itself further divided, it is
called simple (or primitive), otherwise it is compound.
The order is the number of tiles used. When describing solutions, it is convenient to use a notation called Bouwkamp code. One lists the side lengths of the tiles as they appear in the solution, in left to right order, top to bottom, bracketing groups with flush tops. There is a nice article in Martin Gardner's 1962 book More Mathematical Puzzles and Diversions, in chapter 17: Squaring the Square  by William T. Tutte, from Gardner's November 1958 column in Scientific American. Stuart Anderson of New South Wales has a great website called www.squaring.net where he discusses this topic in depth, and gives lots of historical information. Some of the diagrams below are adapted from Stuart's site. The topic is also discussed at mathworld.wolfram.com. In 1925, Zbigniew Moroń (19041971), of Wraclow, Poland, published a paper, 'O Rozkladach Prostokatow Na Kwadraty' (On the Dissection of a Rectangle into Squares), in which he showed a simple perfect squared rectangle (SPSR) of order 9. Reichert and Toepkin (1940) proved that a rectangle cannot be dissected into fewer than nine different squares (see Steinhaus 1999, p. 297). I have the plastic Perfect Squares (Le Carre Parfait) puzzle by Dollarama (China). It's got 9 pieces to be packed into a tray. I measured the tray cavity and the piece dimensions, and allowing for measuring error, manufacturing tolerances, and gaps so the pieces can be easily manipulated, this is an example of the Moroń 1925 SPSR.

Robert Wainwright presented the Partridge Puzzle at the second Gathering for Gardner, in 1996.
Partridge puzzles call for the dissection of a large square into a set of smaller squares, without voids, such that one small square tile of size 1^{2} is used, two of size 2^{2} are used, three of size 3^{2} are used, up to n of size n^{2}. Kind of like the "Partridge in a Pear Tree" song, the number of square tiles of each size increases by one at each step. They're based on the following mathematical equivalence:
Bill Cutler, using a variation of his BOX program, found that the smallest value of n for which a packing exists is 8, that there exist 2332 distinct order8 solutions, and that there are no order7 solutions. Ed Pegg has an interesting article on Partridge puzzles on his Mathpuzzle site. There's also some information at Erich Friedman's site. Kadon sells some of Erich Friedman's Partridge puzzles. Here is an order 8 puzzle I bought from Robert Wainwright at the 2007 NYPP:
Erich Friedman also discusses AntiPartridge tilings. In an AntiPartridge Puzzle, one must dissect a square using n copies of a 1x1 square, (n1) copies of a 2x2, (n2) copies of a 3x3, etc., through 1 copy of an nxn. They're based on the mathematical equivalence:
There exist solutions for (n,k) of: (1,1), (6,14), and (25,195)... The (6,14) square was found by Colin Singleton in 1996.

Another type of squarepacking problem,
discussed by
Ed Pegg Jr.,
is to find the minimal side m of square m^{2}
into which one can pack one of each square of sides 1, 2, 3, ..., n.
In this problem, there can be voids.
In fact, in this type of problem packing the large square without gaps is not possible.
The
only series of squares which sum to a square is for squares of sides 1 through 24,
which sum to 70^{2} = 4900.
(This is also the only number that is both square and pyramidal  i.e. 4900 balls can make a square,
and also be stacked in a squarebased pyramid with layers of 1,4,9,16, etc. 
proved by G. N. Watson in 1918.)
A proof that no perfect tiling of the 70^{2} with squares 124 exists was done in 1974 using
exhaustive computer search by Edward M. Reingold (Gardner 1977).
The Sloane sequence A005842 gives a(n) = minimal integer m such that the m^{2} square contains all squares of sides 1, ..., n. This problem has practical applications, such as electronic circuit layout. Minami Kawasaki gives a catalogue of known solutions. From Ed Pegg, here is a packing of 151 into a 214x214:

The Calibron Twelve Block Puzzle was made by Calibron Products of West Orange, N.J. ca. 1932. I don't have one, but the dimensions of the pieces are shown on Iwase's site. I've been intrigued by this puzzle for some time and I thought I'd cover it here. If you search Google Books for calibron puzzle, you will find links to an ad for the puzzle, selling for $1, in the Jan 1935 issue of Popular Science magazine, an entry for the puzzle in the Catalog of Copyright Entries showing the puzzle was copyrighted on Dec. 22 1932, and an ad in the 1933 New Yorker Vol. 9, claiming that the puzzle has "Baffled over 900 scientists at a recent convention." About.com says that the company Calibron Products was "established by Theodore Edison (18981992) [Wikipedia] [bio at nps.gov] to keep some of his late father's employees and engineers working together on research projects." Theodore's obituary in the New York Times on Nov. 26 1992, says he was the last surviving child of the inventor Thomas Alva Edison. From the inside of the box: "The problem is to arrange the twelve blocks to form a single large rectangle. Any rectangle will do, provided that all twelve blocks are used... We guarantee that there is a straightforward, accurate solution of this puzzle in a single plane, and without recourse to any kind of trick... However, in spite of the enormous number of possibilities, there appears to be only one basic arrangement which satisfies the above conditions... We once offered $25 for the first solution of this problem and distributed hundreds of puzzles at that time,  but recieved almost no correct arrangements! We should like to hear from you if you succeed in making the rectangle unaided." Here is a list of the 12 pieces, using halved dimensions:

Why not buy or make a set of pieces and try this puzzle yourself, before looking at the solution hidden here?


Josh Jordan was kind enough to send me a copy of the Calibron 12Block Puzzle remake produced by Pavel Curtis. Thanks, Josh! For the remake, Pavel has used my halved dimensions. Pavel has posted an interesting writeup of the Calibron puzzle. 
You can buy a nice wooden version at
Creative Crafthouse.

Carlos Rivera, on his website
www.primepuzzles.net,
poses an interesting question about
"prime squares" 
Is there any SPSR or SPSS having only tiles with primenumber side lengths?
The answer is no. Arthur Stone proved that in a perfectly squared rectangle (or square), with at least two square elements, at least two elements have even sides. His proof is on pages 149150 of "Squared Squares: Who's Who & What's What" by Jasper Dale Skinner, II, published in 1993. ISBN: 0963656902. Here is another negative result... While messing about with planar tilings, it's natural to think about extending the problem into 3 dimensions. Can a cube be dissected into a finite set of distinct subcubes? The answer is no. This problem is discussed in Martin Gardner's article, and also online in an article by Ross Honsberger. Proof: Assume a packing of a cube using a finite set of distinct subcubes can be done. The bottom layer will contain a set of cubes, and one of them will be the smallest in that layer. That smallest cube cannot be along an outside edge  i.e. touching a side of the container (other than the bottom)  because if it was, then there would have to be an even smaller cube next to it. Think about it  there are two cases: either it would be in a corner, against an outside wall and with a larger subcube next to it, or along an edge with a larger cube on either side of it. In either case, one side of the smallest cube is bordered by walls extending past it. So, any cube that could fit against it must be smaller than it, which violates our premise that it is itself the smallest in that layer. That means it must be somewhere in the interior, bordered on four sides by a larger subcube. That, in turn, means that its upper face must be completely walled in (again, think about it  every bordering cube is larger than it is, but they're all lying on the same plane as it, so the sides of all its neighbors rise above its upper face). That means that its upper face has to be covered by a set of even smaller cubes. Now, if you think about this state of affairs, you'll see we can start all over again with the previous logic  that covering set itself must contain a smallest member which cannot be on an outside edge... This goes on indefinitely, requiring an eversmaller set of subcubes, and proving that the original assumption is false.
Now, this doesn't mean we can't have fun in 3 dimensions...

Pack It In  Thinkfun This is "Conway's Curious Cube" which calls for three 1x1x1 cubes and six 1x2x2 blocks to be packed into a 3x3x3 box. There is only one solution  see this source. 
Nine rhombic pieces fit in the tray. This is isomorphic to Conway's Curious Cube. 
17 piece packing cube Another John Conway design. 5 of 1x1x1, 6 of 3x2x2, 6 of 1x2x4. Fit into 5x5x5. The same pattern should show on all sides. Gemani calls this "Made to Measure." I've also seen it as "Shipper's Dilemma." 
Conway Box Deluxe This is a nicer version of the 17piece Conway cube. 
The Meiji Caramel puzzle is a version of AntiSlide designed by William Strijbos. Pack 15,14,13, or 12 of the 15 1x2x2 pieces into the 4x4x4 box such that none can slide in any direction. There are no solutions using less than 12 pieces. Using 12 pieces there are only three solutions, but using 13 pieces there is only one solution. This puzzle won 2nd place in the 1994 Hikimi Wooden Puzzle Competition. Purchased from Torito. 
36 piece Packing Puzzle 
T Party  B&P 
Loyd's Cube  Sam Loyd An IPP Puzzle from Jerry Slocum 
LBert Hall Pack the nine identical pieces into a 3x3x3 cube seated in the box. Each piece is a concave tricube with holes and one dowel. This was designed by Ronald KintBruynseels for IPP27, and made by Eric Fuller. The pieces are made from Cocobolo and the box is made from Lacewood. 
"The Five Minute Puzzle That Might Take a Little Longer" Designed by Andy Turner Entered in the IPP 2009 Design Competition Made by Eric Fuller, from Oak (box) and Paduak 
Wim Zwaan  Octahedron and Tetrahedron Fit the Wenge tetrahedron into the Baltic Birch plywood Octahedral box. Then get it out again. Since the opening and the tetrahedron are not quite regular, this is more difficult than it might at first seem. Purchased from Wim at IPP28 in Prague. 

Mine's Cube of Cubes Designed by Mineyuki Uyematsu in 2004. Exchanged at IPP24. 14 pieces pack into a 5x5x5 box. 2 solutions. 
Mmmm Pack the four Mshaped pieces into the box and close the lid. Designed by Hirokazu Iwasawa (Iwahiro). 
Mmm Pack the three Mshaped pieces into the box and close the lid. Designed by Hirokazu Iwasawa (Iwahiro). 
Logs in Box designed by Vesa Timonen Produced by Hanayama in their "Woody Style" line. 
These puzzles are all based on the same design:

Cherry Cocktail Pack six pieces  3 each of 2 kinds  plus the "cherries" into the "glass." Purchased from Irina Novichkova at IPP28 in Prague. 
Thick 'n' Thin No. 7 Purchased from Serhiy Grabarchuk at IPP28 in Prague. 

Bermuda Hexagon designed by Bill Cutler in 1992 (using a computer), made by Tom Lensch 12 pieces to be packed into the hexagonal case in 3 layers. This design was awarded the 3rd prize in the 1992 Hikimi Wooden Puzzle Competition 
"Old Hand Cranes 1 Gin" Eight different blocks to be packed in the wooden Sake cup designed by Nob Yoshigahara produced by Hikimi 

Cubes in Space, designed and exchanged at IPP32 by Hirokazu Iwasawa (Iwahiro), made by DYLANKobo An antislide challenge. 
This is one of Trevor Wood's Teaser Tiles puzzles. Nine tiles, each composed of two slightly different sized layers, with various overhangs. The objective is to fit the pieces flat into the box  i.e. so that all pieces have their two layers parallel to the bottom of the box. Obviously, the particular juxtaposition of piece edges and overhangs will be crucial. Thanks, James! 

Hoffman's Packing Box, or The Inequality of the Means Puzzle  produced by Creative Crafthouse Fit the 27 identical blocks into the frame.
Based on the fact that the arithmetic mean of three values a, b, and c is always greater than or equal to the geometric mean of those values.
Symbolically, (a+b+c)/3 >= (abc)^1/3

Nob's Never Ending Build a cube within the box, from 8 similar angled pieces. The one on the left is a rough handmade version  an auction win. I recognized this in a pic of Matti Linkola's exhibition, and found it on Trevor Wood's site. It is a copy of Nob's Neverending puzzle. Torito sells a version made by Himiki. 
Make Room  variation of Stewart Coffin's #127, by Mr. Puzzle Australia Craftsman version in fine exotic woods  the box is a waxy wood called Yellow Leichardt. Four challenges:

This is TubeItIn by William Strijbos. (Photo from John Rausch's site.) 
The Morph A cube dissected into four clever pieces can morph into three different solids to fill the compartments in the case. According to Bernhard Schweitzer, who sells a copy, this was designed by Boris A. Kordemsky of Russia. I believe this was issued by Bits and Pieces quite some time ago, but I am not sure. I found my copy on auction. 
Funny Cubes  designed and made by Tom Lensch. Purchased at IPP 29 in SF. Each piece consists of two attached rectangular blocks that can be rotated relative to each other. Fit the blocks into the square tray so that the top pieces also form a square. 
Devil's Gate  designed by Ferdinand Lammertink, made by George Miller Purchased from George during a visit to the Puzzle Palace during IPP 29. This is a version of the Langford problem. Find lots of info on the Langford problem here. 
George Bell's Nine Bed Nightmare assembly puzzle (May be available from Puzzlewood.de.) Pieces bot. to top, L to R: A, B, C, D, E, F, G, H, I. Challenges:

Eric Harshbarger's Digits in a Box Ten size 1x3x5 digits  just pack them into a 5x5x5 box. The first version, with pieces lasercut from colored acrylic, was exchanged at G4G9  I purchased a copy at Eureka. Popular Playthings now offers a nice massproduced version. 

16 Hexominoes in a Twin Square, designed and made by Marcel Gillen, exchanged at IPP32 by Carlo Gitt 
Lomino Cube 4, designed and exchanged at IPP32 by George Bell, made by Ponoko 
O'Beirne's Cube, or "Morph 2"  designed by T.H. O'Beirne, made by New Pelikan Workshop, exchanged at IPP32 by Peter Hajek 
Paul Stevens of Wisconsin kindly sent me a copy of a puzzle
he designed and made called the 8in1 Puzzle. It is made from recycled wood and comprises eight pentacubes and a twocompartment box. All but one of the pentacubes are nonplanar. Select any seven of the eight pieces then pack them into the 3x3x4 compartment, allowing a single 1x1x1 void. It is quite challenging! Thanks, Paul!

Bunchgrass Packing Puzzle "13/14" A box with 5 pieces made of spheres  the pieces fit in the box with or without a single sphere piece. They also can form a squarebased pyramid. It is called the 1314 puzzle since with the single sphere there are 14 pieces and 13 without. 
For Your Own Sake  Hikimi (Japan) This puzzle poses the additional challenge of embedding 3 marbles. 
Dragon's Eggs  Pentangle Find a way to pack everything into the box so that the three "eggs" are all concealed. 
Slot Machine  Stewart Coffin #185 obtained from Henry Strout Build a cube within the box, fitting the pieces in through a small slot in the acrylic cover. 
18Piece MiniCubeBlock Puzzle Set 
Four Square Fit the four duallayer pieces into the tray. 
Back in the Box A dissection of a cube into various tetrahedra. 
Mosaic  IQ Puzzles (Family Games) 
Third Degree  Bits and Pieces Designed in 1995 by Bill Cutler, who calls it the "3Piece Blockhead." Discontinued. 
Stark Raving Cubes / Sneaky Squares / Blockhead / Blockout I bought mine from ISHI. Designed in 1983 by and still available from Bill Cutler. Thinkfun's Blockout is a nice, portable, inexpensive copy. Awarded the Grand Prize at the 1986 Hikimi Wooden Puzzle Competition. 
Three Pins By Jean Claude Constantin. Fit the six pieces in two layers into the tray, aligning holes so that the three pins can be inserted, each through two pieces. 

Pack 6  Eric Fuller Entered in the IPP 2003 Design Competition. 
Sandwich  Vaclav Obsivac 
HCP1  Vaclav Obsivac 

Malaga Box  Philos By Markus Goetz. 
Barrel Puzzle From Brian Menold at Wood Wonders 
Stack the disks to form a cob. This seems to be a copy of the Toyo Glass puzzle "AMaizeIng." 
Booze Crate 
Something Fishy also in wood  Fisherman's Dilemma, from Creative Crafthouse 
A nice little packing puzzle handmade in the Ukraine. Purchased off eBay. I'm not sure, but I think this is the same puzzle as shown on www.golovolomki.ru in the Wooden Puzzles section, called "Disobedient Particles" by I.A. Nowitschkowa. 
6piece packing (Krasnoukov?)  from Rick Eason 

Dice Box  Sticks 
Dice Box  Prisms 
Trevor Wood's Cube the Square  unknown craftsman The 8 pieces form a 4x4x4 or an 8x8x1. 
Nob's LL Puzzle  unknown craftsman Each of the 8 pieces is made from two L tricubes. They pack a 3x4x4 box, made from purpleheart. 
Boxed LUV Stewart Coffin #189 a cheap Asian copy, but functional 
Russian 3piece packing Obtained from Rick Eason at NYPP 2008. The label is in Cyrillic and I cannot read it! I'm not sure, but I think this is the same puzzle as shown on www.golovolomki.ru in the Wooden Puzzles section, called "Pythagorean Trousers 2" by I.A. Nowitschkowa. 
This is Packman by Gary Foshee. Get all of the elements into the cube so that all of its surfaces are flush. (Photo from John Rausch's site.) 
Meiji Apollo Fit the plastic candy replicas into the box in two layers. Purchased from Torito 
Oskar van Deventer's TwoPiece Packing From Bernhard Schweitzer at NYPP 2008 
Quadron by Naef (1987) Designed by Jost Hanny 
Fragmented Cube  Oskar van Deventer Pack eight pieces into the box. They can be packed such that faces appear with and without "holes." Purchased from Oskar at IPP28 in Prague. 
Magellan  Philos Designed by Georg Pfaffinger 12 pieces pack into the 4x4x4 box and leave a 2x2x2 hole in the center. Includes other challenges. Purchased at a puzzle store in Prague. 
Caboose, designed, made, and exchanged at IPP32 by Henry Strout 
Nine Parts Packing, designed by David Goodman, made and exchanged at IPP32 by Dor Tietz 
Six Cushion Shot, designed and made by Wayne Daniel, exchanged at IPP32 by Marti Reis 
Tetracubed, designed by Robert Reid and George Miller, made by Wayne Daniel, exchanged at IPP32 by Stan Isaacs 
Pack six pieces in the box, from Japan  purchased at IPP32 (I don't know the name or the designer) 
Hikimi "For Your Own Sake" 21 A sixpiece "squashed" variant of Conway's Curious Cube  contains two voids when solved. 
Super Box 2, designed by J.C. Constantin. Pack the six pieces in the tray so none stick out. The dimensions are such that several arrangements seem like they might fit if you just force the pieces a wee bit  but do not! The solution does not require any forcing at all. 
P26 Drehcube, designed by J.C. Constantin. Arrange the six pieces in the tray and form a 3x3x3 cube. Each piece is composed of four unit cubes and a halfcube triangular prism. On five of the six pieces, the triangular unit can be rotated in place to add to the confusion. 
IQ Fit from
Smart Games.

Back2Back  designed by Raf Peeters, issued by Smart Games Place the pieces into the board, using both sides of the board. A polyominotype packing puzzle, but with an added dimension  the pieces have some units that push through the grid and occupy spots on both sides, and others that occupy a spot on only one side, allowing another piece to overlap on the other side of the board. 
I found the IQ Steps in a local Barnes and Noble. It is another puzzle designed by the incomparable Raf Peeters and issued by Smart Games. 
I found photos online of two instances of the vintage puzzle.
In both cases, the cover is quite faded.
However, one can make out the "Parcel Post Puzzle" title, and the words "Trade Mark" below it.
The truck drawn on the cover is consistent with the style of trucks circa 1913.
I also found a photo of a button celebrating the 1938 25th anniversary of the parcel post service.
However, the style of truck from 1938 is very different from that depicted on the puzzle cover, so
I think the puzzle dates from the earlier period.
The Japanese company Toyo Glass issued a series of packing puzzles using glass elements (usually an assortment of plastic pieces which must be packed into a glass container). I have these unless otherwise noted. Much of the Toyo lineup has been reissued by Beverly (www.been.co.jp)  a Japanese vendor. Puzzlemaster.ca carries them.
[A] means the Glass Puzzle Answer Book contains a solution.
[B] means a reissue is available.
Packed in Tokyo I got this in Japan. 
Java Tea [A] 
Packing Peanuts [B] 
Shot You 
On the Rocks [A] 
Pack the Asparagus Designed by Nob Yoshigahara Related to Tridiamonds 
Pack the Beans [B] (I don't have this one.) 
Pineapple Delight [A] [B] Related to Pentominoes 
Pack the Pudding (or Custard) [B] 
Pack the Beer [B] 
Pack the Plums [A] [B] 
Pack the Peanuts [B] 
AMaizeIng [A] [B] 
Pack the Rice Crackers [A] [B] 
Pack the Orange [A] (I don't have this one.) 
Home Alone Husband 
Bin Cross [A] 
A regular polygon is a closed twodimensional shape having some number of identical linesegment sides, joined at identical angles. They begin with the equilateral triangle, and proceed with the familiar square, pentagon, and hexagon, then continue with the perhaps less familiar heptagon, octagon, nonagon (or enneagon), etc.
Polyforms (Wikipedia entry) are pieces made by joining multiple copies of a given unit element which is a polygon. In the most straightforward cases, the unit elements are regular polygons and they are joined along full edges. These are also known as animals. The pieces can be distinguished by whether they are convex or nonconvex. A piece is convex if you can join any two points inside the figure by a line segment that also lies entirely within the figure. Also, if a piece is distinct from its mirror image, it is chiral, otherwise it is achiral.
Polyforms can also be constructed using threedimensional unit elements, such as cubes or spheres, and these are referred to as solid polyforms. Solid polyforms made from unit cubes are polycubes. Read about polycubes at The Poly Pages. When solid polyforms are constructed, some of the pieces will have all their unit elements lying in one plane, and others will not. The former are planar pieces, and the latter are nonplanar pieces.
Twodimensional polyform puzzles utilize some set of polyform pieces to create a given twodimensional shape. Only three regular polygons can be used to tile the plane without holes  equilateral triangles, squares, and hexagons. Naturally, most polyform puzzles have utilized pieces composed of such units, but other polygons can be used. Here are some of the betterknown planar polyform types:
The polyominoes start with a single unit, called a monomino. Two units joined along a full edge make a domino; three a triomino or tromino, four a tetromino, and five a pentomino. The set of all possible tetrominoes are the shapes used in Tetris. Note that the dominoes referred to here lack the patterns of a conventional set of dominoes, and as a rule, polyomino puzzles do not typically employ pattern constraints other than the occasional checkerboard coloring.
Enumerating Polyforms
Sloan's sequences given for: # free . # 1sided (holes allowed) Wolfram links at top show initial pieces; links in table to Wolfram, Ishino's site, etc. show all pieces 

n, prefix  iamonds #A000577 .#A006534 Wolfram 
ominoes #A000105 .#A000988 Wolfram 
hexes #A000228 .#A006535 Wolfram Wikipedia 
aboloes (tans) #A006074 Wolfram Esser 
cubes #A038119 .#A000162 Wolfram 
Comments 
2 d[i] 
1.1

1.1  1.1  3  1.1 
Dick Hess designed
a puzzle using nine
planar tridiamonds.
The Naef Favus puzzle pieces are a set of planar and nonplanar solid tridiamond prisms. (Labeled dominoes are discussed in the Pattern section.) 
3 tr[i] 
1.1  2.2  3.3  4  2.2  The two triominoes consist of one threeinarow and one "L"  the L is nonconvex. 
4 tetr[a] 
3.4  5.7

7.10

14.22

7.8

Tetromino sets: Tenyo BtC #783
See my diagram of polyhexagons up to tetrahexes. Naef's Hexagon puzzle uses the set of 7 free tetrahexes, made from metal nuts. The Snowflake puzzle by Stewart Coffin uses the set of three trihexes and seven tetrahexes. Michael Keller shows some figures and solutions made with the set of tetratans. The Eternity Delta puzzle is a commercial set of 14 tetratans. Kadon's Tan Tricks I includes 2 monotans, 3 ditans, and the 14 tetratans. Jurgen Koeller discusses tetracubes. The eight tetracubes are named: I O L T N, towerright, towerleft, and tripod. They can make two boxes: 2x4x4 (1390 solutions) and 2x2x8. A set called Wit's End was produced by Lowe in 1967. Piet Hein's famous Soma cube uses the six nonconvex tetracubes plus the single nonconvex tricube. 
5 pent[a] 
4.6

12.18

22.33

30.56  23.29 12 planar 17 nonp 
Ishino's page on pentiamonds.
Peri Spiele (Austria) makes a set of 19 niamond pieces packed into a StarofDavid tray. The set includes two tetriamonds, seven pentiamonds (all 4 possible + dups), six hexiamonds, three heptiamonds, and one octiamond. The 12 planar pentomino pieces are named by convention after the letters they resemble: F I L N P T U V W X Y Z. There are too many commercial pentomino sets to mention. Ishino's page on pentahexes. Commercial sets of pentahexes: Tenyo BtC #22, HiQ Fusion, HiQ Confusion Kadon's Tan Tricks II includes the set of 30 pentatans. There are 29 pentacubes  12 planar (corresponding to and named like the pentominoes) and 17 nonplanar. Stewart Coffin on solid pentominoes; Stewart Coffin's Unhappy Childhood puzzle Kadon's page naming the planar pentacubes; Kadon's page naming the nonplanar pentacubes 
6 hex[a] 
12.19

35.60

82.147  107  112.166 
Ishino's page on hexiamonds.
Hexiamond sets: Tenyo BtC #6 Hexomino sets: Tenyo BtC #600, Spear's Multipuzzle George Miller sold a set of 82 hexahexes. Kadon's Tan Tricks III includes the set of 107 hextans. Kadon sells a set of 166 hexacubes. Livio Zucca's Sexehexes (not polyforms) 
7 hept[a] sept[a] 
24.43

108.196  333.620  318  607.1023 
Ishino's page on heptiamonds.
Heptiamond sets: Tenyo BtC #24 Kadon sells a set of 108 heptominoes. Peter Esser's page of the 108 heptominoes. 
8 oct[a] 
66.120  369.704  1448.2821  1116  3811.6922 
Kadon sells a set of 66 octiamonds.
Ed Pegg Jr.'s page on octiamonds. Kadon sells a set of 369 octominoes. 
9 non[a] enne[a] 
160.307  1285 .2500 
6572 .12942 
3743  25413 .48311 
George Miller sold a set of 160 noniamonds. 
10 dec[a] 
448.866  4655 .9189 
30490 .60639 
13240  178083 .346543 

11 endec[a] 
1186 .2336 
17073 .33896 
143552 .286190 
46476  1,279,537 .2,522,522 

12 dodec[a] 
3334 .6588 
63600 .126759 
683101 .1364621 
9,371,094 .18,598,427 
Perhaps the best known variety of polyominoes are the Pentominoes. Hexominoes and Heptiamonds are also used in puzzles, but the number of pieces quickly becomes unwieldy as one goes up from there.
Basic pentomino challenges include fitting the pieces into a rectangle, or a square with some holes. You can also form large models of each pentomino!
If you become bored with the basic pentomino puzzles, several people have devised more interesting challenges...
Often Pentominos are presented as a packing puzzle, but they are very versatile. If they are made from unit cubes, they can be arranged either flat or in 3 dimensions. However, the 3d constructions do not really interlock due to the limited size and convolution of the pieces.
Concept 5 
Yasumi 
University Games Pentomino Set 
Logika 
Kohner Hexed (thick and thin versions, and alternate cover) 

ChocaBloc  from Kidult A Pentomino set  the 12 pieces resemble chocolate bar pieces and can be flipped over. Presented in a clear 6x10 case. 

Pentomino sets made into games:  
Quintillions, a nice Pentominoes set, by Kadon. This product launched Kadon in 1979. 

ZahlenLabyrinth  Logika 
Camelot (castle pieces on top of flat pentominos  arrange the pieces to build the castle) 
Springbok Pentominoes 
The 12 planar pentominoes can be fit into various rectangles:

The 12 planar solid pentacubes can be packed into various boxes:
See Chapter 3 in Stewart Coffin's The Puzzling World of Polyhedral Dissections. 
Here is one of the 3x4x5 solutions, in case you need to put your set back in its box...
I I I I I X F N L L Y Y Y Y T X V V V T X F N L T X F Y Z T U F N V P X F N L P U Z Z Z T U W N V P U W W L P U Z W W P 
Checkerbox  Bill Cutler 12 checkered pentominoes pack into a 3x4x5 box 
Wit's End by Lowe from 1967 is a set of tetracubes. The instruction sheet gives several construction problems. 
The Spear's Multipuzzle is a plastic set of hexominoes. It includes all 35 "free" hexominoes and duplicates of 7 of them. The pieces are essentially 2D  they are not built from unit cubes and cannot be built into 3D structures. The set comes with a 6x10 tray and a booklet of problems specifying subsets of pieces to be fit into the tray. 
The Ten Yen puzzle, published in 1950 by the Multiple Products Corp. of NY, includes a monomino, domino, both trominoes, and 3 each of the tetrominoes and pentominoes. Kadon offers one. Pieces in three colors. One challenge is to create identical shapes from the sets of three different colored pieces. 
A gift from Brett of three "Meiji Chocolate" plastic Polyomino puzzles by Hanayama  Milk (12 pentominoes), Black (11 hexominoes), and White (8 pieces)  find them at Kinokuniya. 
345 iamonds  designed by Koshi Arai  IPP30 5 sets of the four pentiamonds. The 20 tiles will pack into both sides of the tray  the large triangle, and the doublelayer diamond. 
Tenyo made several polyomino puzzles in their "Beat the Computer" series.
Almost every set has been produced in a variety of color combinations.
Several similar sets have been offered by other vendors as well.
Pascal Huybers has a
webpage showing most of them.
I obtained a group of assorted polyform tray packing puzzles  some of which are duplicates of puzzles shown elsewhere, others of which are tangram and sliding piece puzzles. 
Peri Spiele (Austria) makes a set of 19 niamond pieces packed into a StarofDavid tray. The set includes two tetriamonds, seven pentiamonds (all 4 possible + dups), six hexiamonds, three heptiamonds, and one octiamond. I also found a set that says "Puzzle" instead of "Peri" in the black circle on the box. 
A onemillion pound prize was offered for the solution of the
Eternity Puzzle.
I didn't win. The puzzle comprises 209 pieces called 12polydrafters. For more info on the Eternity series, take a look at 
The Eternity Delta puzzle was billed as a warmup to the full Eternity.
It uses the set of 14 tetratans.
Here are some interesting sites discussing polytans:

This is the Eternity Meteor puzzle. It uses a set of ten pentahexagons. 
Last but not least, the Eternity Heart. 
I believe this is "Hextra" from Robert Longstaff Workshops. It uses a set of septahexagons. This is a gift from Carol Monica, the proprietress of one of the best puzzle shops around  the Games People Play shop in Cambridge, Mass. 
The Snowflake puzzle was designed by Stewart Coffin (#3), and this version made of foam was offered by Binary Arts in 1993. It includes two sets of 3 trihexagons and 7 tetrahexagons, a tray with two levels, and a booklet of challenges. 
Here is an unnamed but colorful set of tetrahexes in a clear case. 
The "Hexagon SenseAGone" is one in a series of Brain Drain puzzles from Mattel. It employs a set of 3 trihexagons and 7 tetrahexagons. The pieces cannot be flipped, and only one of each of the pairs of mirror images is used. The pieces are prettily colored and suggest 3dimensional cubes, but the instructions do not indicate any edgematching constraint. Assemble them / Pack them in the tray. 
This is as good a place as any to show the six Mattel Brain Drain puzzles from 1969 (that I know of)...
Hexagon SenseAGone Assembly 
Profound Round Circle Dissection 
Mangle Quadrangle Edge Matching 
Checkle Heckle Checkerboard Dissection 
Block Shock Edge Matching 
Square Where Packing Equivalent to the Pressman Think Square puzzle. 
Kadon Rombix 
Galt Puzzle Blocks 
TriPentaHexagon  George Miller 



Plexi Roundominoes  issued by Brainwright A colorful set of 28 curvy shapes and a booklet of assembly challenges. Developed by Kadon. 
Plexi Iamondhex  issued by Brainwright A colorful set of 12 angular shapes and a booklet of assembly challenges. 
Piet Hein's Soma Cube is the classic example of the polycube puzzle. The Soma Cube uses the six nonconvex tetracubes plus the single nonconvex tricube. Pictured above are: a pair of plastic Soma cubes from Parker Brothers; a wooden Soma on an aluminum base  the wood is beautiful  dark and striated  I believe it's Rosewood; the green felt base is stamped "Produced in Denmark" though some of the text is damaged; a Soma Cube I made from Lego; SkorMor's Fascinating Cube.
Read about the Soma Cube on:
The Balanced Soma is an assembly such that the pieces remain together when balanced on a single cube
placed at the center of the bottom face.
At least six such constructions exist.
 
The eight pieces of this Baumeisterspiel ("Master Builder") set from Logika include the Soma pieces, plus a 1x1x3. I also have a "mini" version with a handy cover. 
Rhoma is like Soma, but with rhombic pieces. I have a large and a small Rhoma. 
The Illusions from Magnif is similar to Rhoma. 

Here is a link showing the pieces of the Impuzzables. The Impuzzables are also described on p. 3^313 of Kevin Holmes' and Rik van Grol's book "A Compendium of CubeAssembly Puzzles using Polycube Shapes," which also discloses the number of solutions for each. 

Zobrist Cube Set designed by Al Zobrist A nice magneticclosure box containing 33 plastic pieces and a 56 page booklet specifying over 20,000 puzzles  each either a 3x3x3 cube, a 3x3x4 prism, or a 4x4x4 cube to be constructed from a subset of the pieces. Zobrist Cube Kickstarter www.zobristcube.com 

Bill Cutler's Splitting Headache yields a nice AHa moment when one solves it systematically. I think I bought this at Games of Berkeley many years ago. Discussed on Peter Kaldeway's site. 
Stewart Coffin's Half Hour Cube (#29) see the pieces at Puzzle Will Be Played... ; also see Chapter 3 in Puzzling World of Polyhedral Dissections (scroll down to Fig. 53) 
The TetraCube Purchased from Wingstoys (defunct). Cheap Monkeypod wood. 13 pieces make a 4x4x4. One "L" tetracube, plus 12 pentacubes: 6 planar: F, L, P, T, W, Y, and 6 nonplanar, 3 pairs of mirror images: (using Kadon's naming system) L1 and J1, L2 and J2, and L4 and J4. 

The Bedlam Cube Wikipedia entry 
Bedlam Treasure Chest Gift from Brett. Thanks! 
The Pedestal Problem has cubies joined at an offset, and must be assembled inside fenceposts 

The craftsman Scott T. Peterson of the state of Washington made this beautiful version of Stewart Coffin's Unhappy Childhood (#41) puzzle for me. Of the 17 nonplanar solid pentominoes, 12 lack an axis of symmetry. Eliminate the two that fit into a 2x2x2 box to arrive at the ten pieces of this puzzle. Those ten pieces pack into a 2x5x5 box in 19,264 ways, and can be checkered in 512 ways. Only one of those possible checkerings has a unique solution (one other has no solution and the rest have multiple solutions)  this is the checkering for the Unhappy Childhood. I also obtained a version made by Jerry McFarland, called "Coffin's Cuboids." The diagram will help you pack your set into a 2x5x5 box, though it is not a solution since the arrangement shown won't make a proper checkerboard pattern.


Cube from Melissa & Doug  the same set of planar pieces as the classic Diabolical Cube, which appears in Hoffmann's 1893 Puzzles Old and New. Also see Kevin Holmes' Compendium, page 3^33. 
Metropolis 
Rubik's Bricks 



Naef Campanile Designed by Manfred Zipfel and Cordula von Tettau in 1979. See the Campanile pieces here. 
Professor Brain's Tower Puzzle 10 pieces, different from Campanile. 
Here is a puzzle using pieces made from unit spheres  the pieces stack inside a cage. It is called "Cerebrum." 

Flogik.de Skyscraper This is almost identical to Naef's Campanile (but made with much less quality). In the Skyscraper, piece 'B' has an extra cubie sticking up at the junction. 
Tourelle  designed by Yavuz Demirhan, made by Brian Menold from Sheoak and Cocobolo Fit seven pieces into the frame  1 solution. Similar idea to Campanile but there are no planar pieces and the entryway restricts piece orientations. 
Double Cross (without the tray) (discontinued) from William Waite. Fit the 6 pieces together in 2 layers of 3. I think I actually prefer it without the tray  the pieces mate tightly and seem like they would be difficult to manipulate if they were in a tray. 

Naef Escalon Designed by Jost Hanny. 
Tetris Cube Designed by Matt Campbell, produced in 2007 by Imagination Games and tetris.com. 9839 solutions  confirmed by BurrTools. This is the smallsized cube. 
Eclecticube  Kevin Holmes 

Double Take  Mag Nif 2003 Eight pieces form a 4x4x4 cube or an 8x8 square. 
Albertuv #4 The eight octacubes form a 4x4x4 cube or an 8x8x1. Purchased at a puzzle store in Prague. 
Albertuv #8 The eight octacubes form a 4x4x4 cube or an 8x8x1. Purchased at a puzzle store in Prague. 

KeshIQ erasers mfd by Seed Co. in Vietnam. Purchased from Eureka 
Dollar Tree Hexagon Equiv. to Naef Favus at a fraction of the cost! (Favus was designed by Toshiaki Betsumiya.) 
Japanese hexagon An Asian version of the Hexagon/Favus. 

Werkstattwürfel 1 Designed by Bernhard Schweitzer 
The Question Mark Puzzle from Pentangle  six pieces form a cube in two ways, and also fit into the 3x6 box to form a question mark shape.  This is equivalent to the Steinhaus (aka Mikusinski's) Cube. 
Cube Conundrum from House of Marbles Purchased at the Vermont Toy Museum in Quechee Gorge Village. 

Rubik's Puzzle  MegaHouse 2010 Nine planar polycube pieces, stickered using standard Rubik's colors; also a clear cubic container, and instruction sheet (in Japanese). Includes an "official" 1x1x1. Also 2 1x1x2, 3 tricubes, 2 tetracubes, and 1 pentacube (the 'F'). The pieces can be assembled into a 3x3x3 where the six faces are colored as a standard Rubik's Cube. 
4 Uni Cubes  idea by Marcel Gillen, Program by Georges Phillippe IPP18 (Tokyo) exchange puzzle from Luc De Smet Includes 7 plastic polycube pieces  the O, L, and T tetracubes, and four pentacubes  two mirrorimage pairs N1 and N2, and S1 and S2. Comes packed in the box in a 2x4x4 arrangement. Five challenges  you can remove each of the four pentacube pieces in turn and with the remaining six pieces make a 3x3x3 cube; also, find an alternative to the 2x4x4 solid. 
A 7piece cube by Galley Games. 
There are several interesting polycube puzzles I do not have:
Assembly puzzles need not be made just from unit cubes combined in pieces to build a yet larger cube  spheres are another common building block, as are building blocks derived from tetrahedrons. The "pyramid"  or more correctly, the tetrahedron  has proven to be a popular shape for assembly puzzles. Vendors seem to like to capitalize on the mythos and mystery associated with the famous Egyptian pyramids, despite the fact that most of their puzzles are actually tetrahedral in shape rather than pyramidal. The two diagrams to the right show how each shape looks when "unfolded"  you can see that though the pyramid (on the left) and the tetrahedron (on the right) both have triangular sides, the pyramid has a square base while the tetrahedron has a triangular base equal in size and shape to its sides. 
Here are several "pyramid" puzzles that while each posessing only a few pieces, nonetheless can prove to be quite puzzling!
This is the classic twopiece tetrahedron patented by Edward T. Johnson in 1940
(U.S. Patent
2216915).
It was popularized in the following decade when a small plastic version became available from FUN Inc. of Chicago, starting in 1956, and has been produced ever since. The classic 2piece pyramid has to be one of the most simple yet elegant puzzles devised. Once you've solved it, it gets old, but it is always fun to watch a newbie's first encounter with it! 

Many other examples have appeared  here are a few I have...

Fire  designed by George Hart A twopiece dissection of a tetrahedron using a helical cut  this large but loosefitting 3D printed example served for two months as a handson exhibit in a gallery at Stony Brook University. A gift from George  thanks! 

From the twopiece, things escalate...
Here are two examples of an interesting tetrahedron  which, when assembled, will have a void inside. It has three identical (and very pointy!) pieces.




The Pyramidal Pile or Setting Hen suggested by Stewart Coffin, made by Brian Menold at Wood Wonders, from Holly and East Indian Rosewood. The units are truncated rhombic dodecahedra. See Stewart's discussion of puzzles made from rhombic dodecahedra . 

Distorted Cube / Pyramid Pile designed by Stewart Coffin made by Brian Menold from Poplar Arrange the pieces to fill the box 3 different ways and also make two pyramids outside the box. 
A popular style of pyramid puzzle comprises pieces composed of tangentially joined spheres  these are colloquially known as Ball Pyramids. Piles of unit spheres touching in regular arrangements can be constructed in different ways. In each case, the centers of the spheres will occupy points in a threedimensional grid known as a lattice. The French physicist Auguste Bravais, who lived in the early nineteenth century (18111863), identified fourteen unique threedimensional lattice types, now known as Bravais Lattices in his honor. The angles that can occur between adjacent spheres within pieces will be dictated by the lattice. Ball Pyramid puzzles employ a face centered cubic lattice for both tetrahedral and pyramidal piles.
George Bell has written several articles about polysphere puzzles, published in the Cubism For Fun (CFF) journal.
A [square] pyramidal pile. Each layer i, starting at the pinnacle, will have i^{2} balls in it. The entire pile will have (i * (i+1) * (2i+1))/6 balls in it  Thomas Harriot (15601621) seems to have been the first to figure out this equation. Here are the numbers of balls (with the total for the stack thus far shown in parens): 1 (1), 4 (5), 9 (14), 16 (30), 25 (55), 36 (91)... Note that the smallest pile which can be formed into both a square pyramid, and a flat square, has 24 layers and contains 4,900 balls (that can make a 70x70 flat square)! In 1918, G. N. Watson proved that there are no other solutions. 
See the diagram below 
the first layer of spheres is laid in a hexagonal arrangement.
The second layer goes into depressions formed by the first layer, but will only fit in one of two mutually exclusive subsets of the depressions.
Once we have placed the second layer, we now have a choice as to where to place the third layer.
The lowerlefthand image shows an arrangement where the 3rd layer goes into depressions directly above spheres in the first layer. The lowerrighthand image shows an arrangement where the 3rd layer goes into depressions above holes in the first layer. The former is known as hexagonal close packing, and the latter is known as face centered cubic packing. The face centered arrangement is used for Ball Pyramids and Tetrahedrons. 
A tetrahedral pile. Each layer i, starting at the pinnacle, will have (i * (i+1))/2 balls in it (these are called the triangular numbers). A tetrahedron with i layers will have (i * (i+1) * (i+2))/6 balls in it (these are called the tetrahedral numbers  here are the numbers of balls (with the total for the stack thus far shown in parens): 1 (1), 3 (4), 6 (10), 10 (20), 15 (35)... 
Magnif and others have issued a classic ball pyramid (tetrahedron), comprising four pieces each composed of joined spheres. Magnif calls their version Tut's Tomb.
The German company Pussycat makes a diminutive equivalent version.

Variations on the Tut's Tomb design (where the basic four pieces have been further divided) have appeared in plastic, metal, and wood...

A metal version from Bits & Pieces. The pieces are 2x 1x4, 4x 1x3. The House of Marbles Pyramid Puzzle is a wooden version of this (I don't have). 

A larger derivative called The Lost Game of the Pharaohs also has six pieces: 2x 1x6, 2x 2x5, 2x 3x4. (Pharaoh sculpture not included!) 





Perplexing Pyramids  Gordon Bros. of Fair Oaks CA (c) 1976 item no. 154 Six pieces, equal to the Perplexing Pyramid from Gordon Bros.  but this package includes an additional challenge on the back. Use the six pieces to make what George Bell calls the "Roof" shape, with a 3x4 base. A timely find, as in the July 2014 issue #94 of Cubism for Fun, George Bell coincidentally has an article entitled Pyradox: A Pyramid Packing Paradox in which he analyzes sets of pieces that can form both a tetrahedron and a roof.


Here is a 4piece puzzle called "Der Fluch des Pharao" (Curse of the Pharaoh) by Markus Goetz, made by Philos and purchased from Funagain Games. The pieces actually do interlock but I still categorize this as an assembly rather than an interlocking puzzle. 
Cubikon Ball Puzzle The pieces of the Ball Puzzle from Cubikon are all planar and have spheres joined at 90degree angles. Contrast with the pieces of Fantastic Island which employ 60degree joints. Fit the pieces in the tray, then use subsets of them to make pyramids. 
Kanoodle  SmartGames Fit the pieces in the tray, then use subsets of them to make pyramids. 

Puzzle in a Puzzle Box, designed, made, and exchanged at IPP32 by Thomas Beutner 
Kolossal Pyramid from Kadon Designed by Len Gordon; 12 pieces (8 of one and 4 of another). 47 solutions. I don't have this. 
Twopiece Ball Tetrahedron  a 3D print from George Bell These two pieces do interlock and the tetrahedron snaps and holds together, but I have listed it here with other ball tetrahedron puzzles. 
These more complex pyramidal puzzles are all composed of several pieces.
The Bermuda Triangle, designed by Adrian Fisher and issued by Pentangle, is a five piece wooden tetrahedron. The pieces do not interlock, and there will be voids inside the completed puzzle. (Purchased at Cleverwood for $19.) 
The Tempil puzzle issued by Dalloz is a copy of the Bermuda Triangle. Purchased in auction from the John Ergatoudis collection. 

Pyrra was issued by Design Science Toys (defunct). It has 15 pieces and 3 distinct solutions. 
This is a tenpiece pyramid. No name or manufacturer info on the box, other than "Mindgame." Purchased at New England Hobby. There are at least two distinct solutions, since I found one by hand that is different from the supplied solution. The pieces are composed from two logical units  a squarebased pyramid, and a tetrahedron (slightly stretched). There are a maximum of two tetrahedrons and 3 pyramids per piece. 

The "Bamboo" Pyramid has the same 10 pieces as the Mindgame pyramid shown above. The 10piece has been offered under several brands. I don't have these. 

Gizeh by Siebenstein Spiele  8 pieces. I don't have this. 

This is a 9 piece pyramid. I don't have this. Creative Crafthouse offers a version. 

Pieces of the 9piece design can be combined into fewer pieces  above is a 5piece pyramid. The 5piece has also been offered with an attached cord  I have seen it called Khufu's Pyramid offered by Siam Mandalay. Each apexforming piece has been combined with its adjoining tetrahedron, and pieces in the base are also simplified  two of the squarebased pyramids have been combined with a tetrahedron to form the largest piece in the base. I don't have these. 
Here are the Lupus, No. 5156 from Philos, in which the base has been further simplified to only two pieces, making a 4piece pyramid, and the similar Choups from Dalloz. I don't have these. 

Goki pyramid A five piece tetrahedron with irregular pieces. I don't have this. 
I found this Pyramid Puzzle by Galley Games in a shop in St. Augustine Florida. It is the same as the Goki Pyramid. 
Blue RD Tetrahedron  advertising promo 

An Eraser Pyramid I don't have this. 
This is a 14 piece pyramid. Creative Crafthouse offers a version. I have seen it in various woods and different trays, also a version with a triangular collar piece that I suppose helps hold the assembly together. This has also appeared as the Luxor puzzle. I don't have this. 

I got the PyrPlex from Andy Snowie. 
Philos offers a copy of Snowie's PyrPlex they call Gizeh (not to be confused with the Siebenstein Spiele version)  I don't have it. 

Dollar Tree Pyramid Equivalent to the Pyrra. 
This is the Pyramuddle. It seems to have been offered by Duncan Law circa 2011. I don't have this. 



This is a Pyrix puzzle. Assemble a tetrahedron such that each face is a uniform color, constrained by the fixed threading of the pieces. U.S. Patent 5108100  Essebaggers 1992 
From the same maker as Pyrix, Pyram consists of an octahedron and four smaller tetrahedrons, each having various patterns on their faces. Build a tetrahedron satisfying a pattern constraint. 
The Pyrus Puzzle completes the three offered by Enpros. Like Pyram, an octahedron and four tetrahedrons. Build a larger tetrahedron having each of the four colors appear on every side. 

The following puzzles, while advertised as "pyramids," are of course triangular prisms.  
The 11 piece Beehive Pyramid. I don't have this. 
The 3 piece Pyramid. I don't have this. 
There are various styles of dissection puzzle, but all of them involve some figure which has been cut up, or "dissected." The objective is usually to reassemble the figure. Sometimes the pieces of a dissection are contrived such that an alternative figure can be assembled, too. In some cases, it is even possible to "hinge" the pieces to each other so that both forms can be assembled. See this link at Wolfram for more info on dissections.
The Tangram puzzle is a venerable classic where the real objective is to form various silhouettes from the given pieces. However, this version from Melissa & Doug is presented as a straightforward squaredissection and traypacking problem. 
The Magic Square Make a square from the four identical pieces. According to Frederickson (p.30), this was designed in 1873 by Henri Perigal, who was a London stockbroker and amateur mathematician (18011899). 
Square Up Make a square from the four identical wooden pieces. The pieces come arranged with a small square hole in the center  your task is to find a way to make a square containing no hole. 

Double Square  Thinkfun This is another fairly wellknown design  form a square from 4 pieces, then add a fifth piece (a small square) to form another larger square. This design dates back at least as far as the 1934 Johnson Smith catalogue. 
The St. Charles Milk Puzzle Seven pieces form a square. Discussed in Slocum and Botermans' The Book of Ingenious and Diabolical Puzzles on p.12. 
Dickinson's Witch Hazel A vintage advertising promo. 

The Elusive Square Puzzle  TSL Twelve pieces, whose collective area is 32 unit squares. What does that tell you about the solution? 
The Pythagorean Puzzle
Originally sold in London in the 1840s IPP30 exchange from James Dalgety Use the six pieces to prove the Pythagorean Theorem: For a right triangle, the sums of the squares on the sides equals the square on the hypotenuse.

Snider's Diamond Puzzle The 10 pieces form a square. Discussed in Slocum and Botermans New Book of Puzzles on p.14. 


Super Star  Melissa & Doug This is a dissection of a fivepointed star, in a tray. 
Broken Heart Form a heart from the 9 pieces. 
Doctor's Puzzle Board 
IQ Circle (PeToy Hong Kong) 
Mind Bender Circle 
Squaring the Circle  Dollar Tree 
Perfect Squares 
Profound Round One of Mattel's Brain Drain series. 
Fit the six pieces into the case to form a rectangle such that it contains only 3 straight seams. From puzzlefactory.com. 
Form a sixpointed star using the six pieces. Also from puzzlefactory.com. 
This set of "What's Your Score" puzzles from Shackman includes a dissected cross, square, and form a star. 
Watney's Red Barrel puzzle Build a red barrel from the pieces. A nice symmetric dissection. 
"Jeu de la Croix" is a vintage French boxed version of a dissected cross on a pedestal. 
"La Cocotte" is a vintage French boxed puzzle  form a bird shape from eight isoceles right triangles. 
Bibendum sixpiece rectangle 
"Jeu de lOctogone" is a vintage French boxed dissection of an octogon into 12 pieces. (I don't have this.) 
The "Red Cross" or "Mysterious Cross" puzzle has been issued by several manufacturers of different nationalities and is known by various names. The eight red pieces form a Greek cross. The eight white triangles fill in the corners of the square. 
IQ MegaForm Circle 
The Land Puzzle You are given a 2x2 square, with one corner unit square missing, leaving three unit squares. Cut the shape into four identical pieces. 
Stacked Triangles  George Miller 
Stacked Squares  George Miller 
Flying Saucer, designed and exchanged at IPP32 by Jeremiah Farrell, made by Chris and Walt Hoppe 
Nightmares, designed by Jeremiah Farrell, made by Walt Hoppe Would have been exchanged at IPP32 by Thomas Rogers (deceased) 
PEKE  designed by Kohfuh Satoh Form a Greek cross. made by Saul Bobroff at Here to There Puzzles of Beverly MA. a gift from Saul  Thanks! 
Spear's Shape Puzzles 

Squaring the Circle Jigsaw Puzzle  Copyright 1967 American Publishing Corp. Waltham, MA Not really a jigsaw, since the pieces do not interlock, and each pieces' edges do not uniquely identify its neighbors. Also not really "squaring the circle"  it simply comes with four identical curved pieces to be applied at the edges of a square, trivially making it into a circle. The challenges lies in forming a 9x9 square using the 11 polyomino pieces whose total area equals 81 units. 

Sometimes the objective is just to make a symmetric shape from the pieces (often a shape with just one axis of symmetry)...  
Symmetrick, designed by Vesa Timonen, made and exchanged at IPP32 by Tomas Linden 
Balance of Power, designed, made, and exchanged at IPP32 by Rod Bogart 
Symmetric Shape, designed, made, and exchanged at IPP32 by Emrehan Halici 
Trapezoid Symmetry  designed by Yasuhiro Hashimoto Form 3 symmetric figures using only the two smaller pieces. Then form 5 symmetric figures using all 3 pieces. 
The dissected T has certainly been the most popular, but other letters have been dissected, too.
Missing T  Thinkfun This is a version of the classic 'T' dissection, by Thinkfun. 
Another classic T. 
Pa's T from Drueke. 
This cardboard version of the classic T dissection puzzle is a promotional item for a magician. 
Chase & Sanborn CoffeeTea Showing both sides of each of the four pieces, which form the usual T. 
An H dissection puzzle was included in the vintage "Deluxe Puzzle Chest No. 3006" from F.A.O. Schwartz. 
A political promotion  form the letters F and D. 
The "Famous F" puzzle Note the trapezoidal piece  these pieces ar pretty much the same as in the "FD Puzzle." 
Cracker Jack F (I don't have this.) Similar to the "Famous F." 
Fletcher's F  an advertising promotion. (I don't have this.) Different than the "Famous F." 
Furnas  The New F Form an F from the six pieces. 
Magic Z 
Dad's Boy K (I don't have this.) I've drawn the four pieces. 
An H Puzzle designed by Tomas Linden and made from Marblewood by Eric Fuller. 
LinkBelt M Puzzle 
I was asked for help in solving The New B Puzzle from Gold Star Coffee. Seven pieces form a letter B. I don't have this, but I did figure out a solution. 
Form the word THINK from the 21 pieces. The pieces of each letter are easy to discern since the letter to which each piece belongs is embossed on its face. The T is the classic T dissection. The H is also familiar. The I is trivial. N and K gave some challenge. I also found a copy in its original package. 

New*T, designed, made, and exchanged at IPP32 by Nick Baxter 
The vintage Celestial Cross puzzle issued by McLaughlin Bros. of NY. 

A vintage fivepiece cardboard Number Nine Puzzle, issued by the National Carbon Division of Union Carbide and Carbon Corporation, advertising Eveready Batteries. I have obscured the borders of the individual pieces in the photo of the solution. 

The vintage Red Cross Puzzle is a twelvepiece dissection of a cross (or the letter t).

A dissection of a Rupee sign, designed and made by Scott Elliott 
Greg N. Frederickson is an expert on dissections which transform one shape to another, and discusses them at length in his 1997 book Dissections: Plane & Fancy.
Woodn't Tri  Reiss Form a square from the 4 pieces. Then form a triangle. This is a wellknown dissection, originally called the "Haberdasher's Problem" and created in 1907 by Henry Dudeney. Discussed by Frederickson pp1368. 
Devil Puzzle This set of pieces can also be put together to form a rectangle. It was offered by Bits and Pieces. It was also offered as part of a series by Nob Yoshigahara. This is the same set of pieces as in the Anchor Kobold puzzle. 
Dudeney's Zoo from Archimedes' Lab The triangle, pentagon, hexagon, and octagon are each dissected such that the pieces of each can form the square. 170mm x 120mm. 
The Adams' Square and Cross. Form a square or Greek cross from the four pieces. (I don't have this.) 
Form a square or a Greek cross from the six pieces. An advertising premium from Molson  the pieces are nice 1/8" plastic. Note the similarity to the Adams Square or Cross  two pieces have simply been divided. 
"A Double Puzzle." A vintage advertising puzzle from Dickinson's. It is the same puzzle as the Molson Square or Cross puzzle. 
Mond oder Kreuz (Moon or Cross, aka Crescent or Cross) Make both a crescent moon, then a Greek cross from the pieces. From Wil Strijbos at IPP31 in Berlin. Thanks, Wil! A nice wooden version of Sam Loyd's Cross and Crescent dissection/transformation between the crescent and a Greek cross (plus sign). Notable because of the curved edges accommodated. Notice the flattening of the tips of the crescent. The nice 7piece dissection shown was actually found by Harry Lindgren. It avoids thin slivers and differs from Loyd's solution. Discussed by Frederickson on pp1679. 
Cut Out Puzzle You are given a 2x3 rectangle, with one corner unit square missing, leaving five unit squares. Cut the shape into three pieces, which can be rearranged to form a square. 
Spade and Heart by Mineyuki Uyematsu Make a Spade or a Heart from the four pieces. Purchased at IPP28 in Prague. 
A vintage Cracker Jack premium  the "Chicken and the Egg Puzzle" 
T+3  designed by Hiroshi Yamamoto The 3 pieces can be arranged to form four different pentominoes, including a T. A really nice dissection! This won a Jury Honorable Mention at the 2011 IPP Nob Yoshigahara Puzzle Design Competition. 
Over the years, there have been many variants on the theme of a dissected checker or chess board. Jacques Haubrich has published a compendium of checkerboard puzzles in two volumes. The first volume, "A Century of Checkerboard Puzzles," describes all known checkerboard puzzles  over 440 of 190 different types  published between 1880 and 1980. The second volume, "Additional Checkerboard Puzzle Designs," covers checkerboard puzzles published in the last 25 years.  
Jacques characterizes the puzzles using a code of the following format and meaning:
N^{[2]}.D.SL

Slocum and Botermans, in their 1986 book "Puzzles Old & New" suggest that the first checkerboard puzzle was this Sectional Checkerboard of 15 pieces, patented in 1880 by Henry Luers (231963) and produced by Selchow and Righter. 
This "Krazee Checkerboard Puzzle" was made by The Plastrix Co. Inc. Jamaica NY. There is no date on it, though in Haubrich's "Century" the date listed is 1957. This variation has code 12.11.37. My Dad had a puzzle like this, but it's gone  and I don't remember which variant it was. 
"The Famous Checkerboard Puzzle"  "Only 12 pieces but  Oh My!" 
This is the Bug House puzzle. Jacques gives a date of 1912. This has metal, rather than cardboard, pieces. It was offered in a rectangular box, and in a square box. It has code 14.14.35. 
This one is the "Unique Original Checker Board Puzzle" from the Unique Novelty Company, and not only is it "Improved" but it is also the "Most Difficult Puzzle Known." It has code 14.14.35 and is the same set of pieces as the Bug House. No date is given in Jacques' book, but Slocum and Botermans bracket this in 19301940. 
This one, "manufactured by J. F. Friedel Co., Syracuse, N.Y." calls itself "The Original Checkerboard Puzzle." I have no idea if the claim is true. There are 15 pieces and the price on the box says 10 cents. Jacques gives no date. Code is 15.14.36. 
The Famous and Baffling Checker Board Puzzle has fourteen pieces and originally cost fifteen cents. 1927, code is 14.14.35. Inside the cover, the Vasen Mfg. Company of Davenport, Iowa, ran a contest offering $500 in Gold for the greatest number of correct solutions. Unfortunately, the contest expired July 15, 1928. 
Checkle Heckle is a checkerboard dissection in the Mattel Brain Drain series from 1969. It consists of a tromino, 4 tetrominoes, and 9 pentominoes. The pieces cannot be flipped, so some mirror images are included. This is the same set of pieces as the Famous and Baffling Checker Board Puzzle. Code is 14.14.35. 
Angle Mania has 15 pieces, but only 14 are needed to complete the puzzle. Four different pieces can be left unused. From 1984. Code: 15.15.26. 
This is a recent wooden variation called just the "Chess Box." It includes a set of 12 checkered pentominoes plus a 2x2 checkered square piece. 
Golf Tease  Great American Puzzle Factory 1996. Assemble 14 pieces into a 9x9 checkered square. 
An advertising puzzle of 14 polyominoes from AMF. 
The older version of the TSL Draughtboard Puzzle. 
The newer version of the TSL Draughtboard Puzzle. 
But  Oh My! 
An advertising puzzle for the Burlington Railroad. 
All Square 
Uneasy Checkers 
Tenyo Checker puzzle 
Tenyo Checker puzzle (back) 
A vintage 12piece Banzee Island Checkerboard Puzzle. An advertising promo for McCracken Realty Inc of Phoenix AZ. 
Sectional Checkerboard Puzzle  a vintage advertising promotion from the PhenyoCaffein Co. of Worcseter MA. "Patented Sept. 7, 1880." This is the 15piece Luers design. 
PhenyoCaffein Checkerboard cont'd 
PhenyoCaffein Checkerboard cont'd 
Andy Snowie's CalmPlex MindBlock is part checkerboard dissection. I made one from LiveCube.
Slocum and Botermans in "Puzzles Old and New" on page 14, and also Ishino's site, describe another variant (I don't have) from 1908 called Broken Chessboard by Henry Ernest Dudeney. Since it is composed of 12 pentominoes and a 2x2 square, as is the Chessbox above, they might be the same.
Here is the 14 piece "CutUp Checkerboard" from Edwin Wyatt's 1946 book Wonders in Wood (I have highlighted the piece borders):
There are several cubic puzzles in the form of a dissected die. In Hoffmann's Puzzles Old & New, The Spots Puzzle is number XVII in chapter III. The puzzle consists of nine 1x1x3 bars, each decorated with some pattern of spots (pips on the die). The task is to assemble a 3x3x3 replica of a die, having the correct arrangement of pips on all six sides. The modern puzzles below are all based on the same principle.  

Intelligence Puzzler 
Cracked Dice  Lakeside 1969 There are three dice  one whole (serves as a prototype) and the other two dissected into three 1x3x3 pieces each. 
Make a Dice Puzzle Can you solve in 8 minutes? Copyright 1957 St. Pierre & Patterson Mfg. Co. 
The Broken Die  Gantt's Wood Things 
made in China 

Twice Dice  Pentangle (small version) 
Twice Dice  Pentangle (large version) 
Woodn't Die  MagNif 
I found another dissected die  it seems fairly old  it comes in a purple box and has nine red pieces with white pips.


A vintage Shackman "Dice" assembly puzzle, with instructions 
"Vegas Baby" cube from SiamMandalay (A gift from my brother.) 
I bought an "8block Collusion" puzzle from
Rocky Chiaro.
Rocky refers to the Collusion and its relatives as "pin puzzles."
I solved Rocky's Collusion and realized it was similar in principle to several other
puzzles in my collection such as Jean Claude Constantin's "The Fence"
that don't necessarily employ pins.
I call this group of puzzles the "Crossed Sticks Family." A set of rods/sticks are crossed in two layers, with the points where each rod crosses (mates with) another constrained by a feature present at that location on the rods, and the compatability of the respective features. The crossings define a grid. Identical overall physical dimensions make the rods interchangeable (except for their features), and features are positioned at crossing points. The notching positions are welldefined along the rod, and the number of potential notch positions is related to how many rods cross. When rods can be inserted only one direction into a frame, I call them "asymmetric." 
The progenitor of this family seems to be this puzzle called Sputnik, made in the 1950s in Japan.

Notched rods can be assigned unique identifiers simply by giving them a binary code  start on one end and compose the code with a zero for no notch and a one for a notch. For three kinds of features, e.g. holes, flats, and pegs, count in trinary, etc. When determining the ID for a piece, my convention is to orient it so that the "endmost" notch is rightmost, and number with the LSB on the right.
The features are drawn from a specific set:
I wrote a program to analyze this class of puzzles. Click here to run my crossedsticks puzzle solver program. It is written in javascript and runs clientside on your computer. (So IE 6 may complain about security  you might have to allow blocked content.)
First choose the "degree" of the puzzle  how many rows (or columns) to model (15), then choose the apropos number and type of pieces from the list. The program is limited to degree 5, and only two rod features. I don't support duplicate pieces, but several pieces are endforend symmetric so there is a way to "cheat." Scroll down the page and click "Run." Each time a solution is found, an alert box will pop up listing the configuration. You can hit OK to continue and find another solution, or Cancel to quit and inspect the current solution in the bottommost graphical area labeled "Inspect."
Symmetry considerations: the program currently does not recognize all symmetries, so it will produce some redundant solutions. However, for a regular grid there are a limited number of distinct locations where the first rod can be placed. The locations can be divided up into a small number of distinct classes, and placing the first rod at any location within a class is equivalent to placing it at any other location in the same class. This allows one to choose an arbitrary single location within a class for the first rod and omit analysis of all other arrangements where the first rod would be in any other location in the same class. I call the classes the "equivalence classes" for the grid and identify them using A, B, and C. Furthermore, for a given set of rods all of which must be used, any rod may be chosen arbitrarily as the first rod to be placed.
You can also use BurrTools to solve this type of puzzle. I programmed in all 16 4position asymmetric pieces for a 4x4 arrangement, along with a frame, and found 408 solutions using various sets of 8, disallowing duplicates and internal voids.
TwoAxis Arrangements, Two Features, 3x3 and 4x4, With a Frame  


Haba Crux Asymmetric Pieces: 0, 1, 2, 6, 12, 13, 14, 15 One solution. 
A nice hefty lucite 4x4 weave puzzle  I found it in Montreal. Pieces: 0, 1, 2, 6, 12, 13, 14, 15. (Same as Haba Crux.) 
This is a cheap monkeypod wood version called the "Snag Box," also known as the "Computer Chip." Pieces: 0, 1, 2, 3, 6, 7, 14, 15. Two solutions. 

Here is another 4x4, called "Weaver's Dilemma." I don't own this puzzle, but I wanted to show it because it uses duplicates of several pieces. Pieces: 0, 2, 2, 3, 6, 6, 15, 15 
A wooden 3x3 weave puzzle from "The Akron Los Angeles CA 90038." Made in Japan. Pieces: 0, 1, 1, 5, 5, 7. 

The Fence Jean Claude Constantin Pieces: 1, 2, 3, 5, 6, 7, 9, 11. 

TwoAxis Arrangements, Three Features, 3x3, 4x4, 5x5, No Frame  


Timbers by Mad Cow Pieces: 010, 120, 200, 201, 202, 220. 
The Log Pile puzzle uses 10 sticks in 2 crossed layers of 5. There are 13 pegs and 13 holes, so no hole/flat or hole/hole matings will be possible. Pieces: 00110, 01012, 02011, 02101, 02121, 10121, 11012, 11202, 11212, 12112. 

ThreeAxis Arrangements  
The "Clive Cube" is a representative of this group, extending it from the 2 axes employed above, to 3 orthogonal axes. 
The "IQ Puzzle" or "Ten Pins" puzzle is another 3D example. 
I got this version from Torito. They call it "Sapience Sticks." 

The Nine of Swords 
This is the plastic Reiss version of the Nine of Swords. 
Arjeu Achille CT5152 Purchased at GPP. 

Special Arrangements  
Haba Verticus  designed by Heinz Meister Ten sticks, with holes or flats at 5 positions. Arrange them in two crossed layers of 5 each, such that holes in both layers all align. 
Rick Eason's Keyhole Puzzle calls for 6 sticks to be arranged in a 3x3 sandwich, but with the additional complexity of sequential assembly. The pegs are screws and the holes are "keyholes" into which the screwheads must slide in the proper direction. 
Rick has taken the keyhole concept into a new dimension with his Keyhole Cube. 

Prismazul Octuple  designed by Ingo Uhl, made by Logika Spiele Exchanged at IPP31 in Berlin by Tanya Thompson, purchased from Tanya. Build a triangular prism with the eight pieces  4 equilateral triangles each with a footprint of 4 unit triangles, and 4 rhombuses each with a footprint of 4 triangles. Each piece can have unit triangles at three different levels: L, M, and H. There are 11 unit triangles at L, 10 at M, and 11 at H. The rhombuses preclude the target shape being a prism like a Toblerone bar, with a crosssection of an edge2 triangle. A triangular prism with a crosssection of an edge3 triangle is also precluded since the available 32 unit triangles could not be distributed evenly. (Each layer would have a footprint of 9 triangles  3 layers uses 27, which is too few, and 4 layers uses 36, which is too many.) That leaves a 2layer triangular prism with a crosssection of an edge4 triangle, giving a layer footprint of 16 unit triangles. This implies that the pieces be arranged in two layers each containing 2 triangles and 2 rhombuses. (The four rhombuses alone cannot tile a side4 triangle, neither can one rhombus with 3 triangular pieces.) If the pieces in the layers are oriented so that their multilevel faces face the opposite layer, then the 10 M units will mate 5x5, and the 11 L's will mate with the 11 H's. The indication that there should be 5 M units in each layer seems like a good clue! 

Alexandre Muñiz contacted me regarding "crossed stick" puzzles. He has designed several, and very kindly sent me examples of his 10piece Decagram, and his 8piece 4Pointed Star. You can read more at his website PuzzleZapper.com. Thanks, Ali! 
Potential new puzzles suggest themselves  extend the set of features to 4 or more, and/or use a different compatability matrix. Use features other than levels, or pegs/flats/holes  how about magnets? A magnet embedded in a rod offers N or S, and the absence of a magnet at a position allows a third feature. I include the compatability matrix for an imaginary Rob's magnetic puzzle below. No magnet = 0, N = 1, S = 2.
Collusion

The Fence

Timbers, Log Pile

Stabpuzzle

Rob's Magnetic Puzzle

These puzzles are slightly different from the previous examples, in that a piece can have "pegs" (or bumps) on both sides.
The puzzle uses six planks of width 1 and length 3 units, and includes two 3x3 plates with all holes. At each of the 3 positions on a side of a plank, there may be a hole (which goes through the plank and therefore also appears on the other side in the same position), a flat, or a peg (which fits into a hole). When the pieces are mated, a peg must mate with a hole from one side, and this blocks BOTH sides of the hole. Two holes, two flats, or one of each may also mate. So a length3 plank has 6 positions at which a hole, flat, or peg could exist. For any plank, there may be a maximum of 3 holes or 6 pegs.
Below is my enumeration of all possible pieces for this style of puzzle. The PrairieDog Town puzzle utilizes 6 pieces, outlined in red in the chart (the piece with 2 bumps and 1 hole, with the hole on an end, is used twice). I have shaded green the cells containing only pieces having at least one pair of opposing pegs.
I have added this category because there are several puzzles that one can argue belong in the assembly section, since they are neither true interlocking puzzles, nor are they true sequential motion puzzles where long operators are needed, yet they do require some backandforth or rotational movement of the pieces, and the order of placement of the pieces can matter.
Crossroad  designed by Goh Pit Khiam and made by Walter Hoppe. Purchased from Walter at IPP28 in Prague. 
Pack the Square, designed by Goh Pit Khiam, made by Joe Sarabande, exchanged at IPP32 by Larry Seidman 
The ODD Puzzle  designed by Hirokazu Iwasawa (Iwahiro). Three pieces (two identical) to pack into the box. Winner of the "Puzzle of the Year" Award in the IPP28 Design Competition. 
Eight Pack  designed by Tom Jolly and issued by Philos Pack eight tetracubes (four towerleft and four towerright) into a 4x4x4 cage. Purchased from a puzzle store in Prague. 
Here is a set of pieces in a cage. I received this puzzle in a trade with P. F. Ramos  he designed it and Interlocking Puzzles (now defunct) made it. It is called Twin Pentominoes Into a Light Box. There are two instances of each of the nonplanar pentomino pieces. 
Pentominoes in Cage from Brian Menold at Wood Wonders 
Closterman cube Six pieces fit sequentially into a cubic cage. Nicely handmade in Yellowheart wood. 
Mine's Cube in Cage from Brian Menold at Wood Wonders 
Framework II  designed by Markus Götz Made by Eric Fuller, from Walnut, Sapele, and various other exotic woods. A redesign by Markus of Markus' original, with analysis by Tom Jolly. This version has a single solution. The pieces fit into the tray which is open on both sides. Offset tabs attached to the piece blocks grip both the frame and other pieces, making this somewhat interlocking and requiring sequential [dis]assembly. 
Brunnenspiel, by Markus Goetz 
Circelei  Hendrik Haak IPP26 Fit three hinged 3layer polyominoes into three stacked trays. 
This is the Lolly Box, designed by Alfons Eyckmans and made by Eric Fuller  a walnut box, with Bubinga, Pau Ferro, Purpleheart, and Paduak pieces. 
On 6/29/13 I had fun attending a puzzle party hosted by Saul and Paulette Bobroff at their home. Several notable puzzlers were there and we all got to play with much of Saul's extensive puzzle collection. Saul kindly gave me one of his IPP31 exchange puzzles  design number 138A by Stewart Coffin  the Piggy Box. Thanks, Saul and Paulette  I had a great time! 
Packuliar designed by Tom Jolly made by Brian Menold Pack the four pieces into the box  a sequential assembly puzzle. No solved image  too much of a hint. 

Core  designed by Yavuz Demirhan, made by Eric Fuller from Sapele and Cocobolo. Fit five pieces into a 3x3x3 cavity in the frame, working through a 2x2x2 opening. 

Boussole  designed by Yavuz Demirhan, made by Brian Menold from Poplar and Cocobolo Fit four pieces into the frame. 
Many assembly puzzles use pieces themselves constructed from regular units  cubes, spheres, or tetrahedrons. An assembly puzzle can also have irregular dissimilar pieces. This section covers a wide variety of unusual assembly puzzle designs.
Each Paracelsus Puzzle is one of a series of unique castings.
I have three  a Disk, an Oil Drop (or Waterfall), and Birds.
I found the following photo of a catalogue page showing seven designs:
I received a request for help in assembling the Waterfall puzzle. Even though every Paracelsus Puzzle instance is unique, the following stepbystep assembly images of my copy might help:


Penthouse from Pentangle 
Screwball (an oldie) U.S. Patent 3813099  Scott 1974 
The "Moron Puzzle" To quote from the label: Morons  Take 1 Min. Idiots  Take 2 Min. Goofs  Take 3 Min. Numbskulls  Take 4 Min. 

Bamboozle  B&P 
5th Chair  Thinkfun (Gift from Brett) 
The Chaotic Cube 

2 Scheibenpuzzle (Logika) 
Heart  Logika 
4piece puzzle  Logika 

Think Tac Toe  Pressman 
Pegged  B&P 
Olistripe The pieces interlock somewhat, but not enough. See U.S. Design Patent D500347 awarded to Daniel R. Oakley in Dec. 2004. 

Thinkamajig Copyright 1974 by Leonard J. Gordon (Gordon Bros.) 
Jumpin' Frog Jumble The pieces do "interlace" but they don't really interlock in a solid 3D structure. 

The Woody Cube (Nankai)  B&P 
The Intragon from Naef Designed by Jost Hanny in 1989. Twelve pieces assemble inside a frame. See the Intragon pieces here. 
Six Key Mine (B & P) An R.D. Rose design. First Prize, 2003 IPP Puzzle Design Competition. The pegs have tongues that can interfere inside the sphere. Insert all 6 without interference. 

Just Fit  William Strijbos 16 pieces plus tray. Create a twolayer 5x5 checkerboard in the tray. 1990 Hikimi Wooden Puzzle Competition winner. 
Diamond Mind  Constantin 
Diamond Soul 

Hippo Haven (Thinkfun) Each Hippo has two pegs. The pegs and holes in the base are of 4 different depths. Find a way to fit the Hippos in the base so all pegs are completely inserted. 
Short Circuit Purchased the Constantin version at GPP. Similar to Hippo Haven. 
Hooked Cube Philos (Goetz) 

Juha Six J's Cube set  IPP19 Together, the 24 pieces from the four cubes can make over 200 assemblies. 

Tower of Babble by Leonard J. Gordon Item No. 134 
The Infernal Triangle was issued by Gordon Bros. and is marked "Item No. 135 1974 Leonard J. Gordon." The seven pieces are similar to those of the Tower of Babble, but here you must arrange them to form a twolayer triangular grid with 5 cylinders along a side. 
Surface 

Harry Potter Mirror (see U.S. Patent 6976678  Setteducati 2005) 
Punch Cards Tom Lensch 
A set of McDonalds promotional puzzles 

Link Puzzle make a cube from the loop of chain links 
Rising Mountain 
This is a sculpture made of South Australian Red Gum wood by Robin Turner. I believe it is one of his "Ayers Rock" series. 

Impuzzleble 
A set of vintage puzzles from PlasTrix of Brooklyn NY, includes: Krazee World, a pair of Batee Baseball, a pair of Krazee Links, a checkerboard dissection, a dissected scene 
Nuts and Bolts  Learningsmith 

Tool Trouble 1996 Great American Puzzle Factory, Norwalk CT. Assemble the 17 irregular pieces into a 7" x 9" (4x4 piece) rectangle. Six of the pieces have diagonal edges. Each piece depicts some tools, but they have nothing to do with the solution. 
Prismentwist  Logika 
Tuned In Milton Bradley 1973 Using all 14 gears, assemble a geartrain linking the knob with the male and female symbols. 

Chess Cubes 
Daily Mail Crown Puzzle 

There have been several puzzles produced based on the theme of two sets of copies of distinctlyshaped pieces, where one set can be used to completely cover the other set (i.e. the sets cover the same area). Some of these are very challenging! This "CoverUp" category seems to have been invented in 2004 by Robert Reid.  
Cover Up (2004) Puzzlefriend Jacques Haubrich kindly sent me a copy of this 8piece puzzle, which he says is the "mother" of this type of puzzle, designed by Robert Reid. 
Cover It Up Designed by Robert Reid; this was Saul Bobroff's exchange puzzle at IPP26, where it won an Honorable Mention in the Design Competition. Cover the dark pieces completely with the light pieces, no overlapping the darks. The total area of dark and light each equals 4x7=28 units. It should be possible... 
Boston Cover Up  designed by Robert Wainwright 

Top This!  Thinkfun This Thinkfun puzzle offers a set of challenges similar to Cover It Up and Boston Cover Up, but simpler. 
A CoverUp variant by Krasnoukhov Purchased at IPP 29 in SF 

Erich Friedman's Cover Up design  three challenges. From Creative Crafthouse 
Another CoverUp variant by Krasnoukhov I don't have this  photo from Lilly Library Slocum collection. I assume there are 3 of each piece. 

MetallWürfel  Constantin 
Times Square  B & P 
Ziggurat  Creative Crafthouse has it. 

Dizzy Tower  Dizzy Art 1996 
Naef's Discon puzzle, designed by Jost Hanny. Also, Discon Fever  a copy of Discon from B & P Peter Kaldeway's site shows a solution. 
I received this nicely made copy of the Discon puzzle, from craftsman Steve Kelsey. Thanks, Steve! 

Barricade  B & P 
This is Mental Block Puzzle #5 Vortex, by R. D. Rose. It is crafted from aluminum and comprises five rings with various pegs and holes around their perimeters, which must be assembled into a cylinder. 
MT5T (Make the Five Tetrominoes)  Mission 1 designed by MINE (Mineyuki Uyematsu) Arrange the four large pieces so that a subset of their gaps exactly enclose the five tetromino pieces. A similar version won a Jury First Prize at the 2011 Nob Yoshigahara Puzzle Design Competition 

Idea Cube  by Idea Ocean 
A paper version of Deep Sea Tango  obtained from George Hart at the 2007 NYPP. 
The 3Q Cube designed by Takeyuki Endo. Fit the three twocube pieces into the cage. 2 solutions. 

Milton Bradley made a couple of "Stickler" puzzles. Insert pins into a stack of disks which have holes at various points. The disks must be aligned so that all pins can be inserted. 
Schalenwurfel  Logika 
Keiichiro Ishino modified Takeyuki Endo's 3Q Cube so that it has only one solution. A gift from Bernhard Schwietzer, at NYPP 2008. Thanks, Bernhard! 

A selection of "Dicebox Mindbender" puzzles by MiToys  HalfCubes, Rod by Rod, and Stacked Sticks, purchased at Eureka, and Cube Mates, from Brett. Imported from China by CHH Games. 
Three diminutive but colorful plastic puzzles from Germany  build a cube from six panels, build a cube from nine concave tricubes, and build a step pyramid. 
9Post Packing Puzzle De Vreugd B & P 

IQ Cube  Brainbenders Eight cubes with tabs and slots. Make a 2x2x2. 
This is a relatively inexpensive massproduced copy of Wayne Daniel's famous All Five assembly. Purchased from Mr. Puzzle Australia. 

Here is a series of assembly puzzles by Andy Snowie:
From left to right, they are: Orbsticle, ConeFusion, CyliPlex, EllipToy, and Pocket CalmPlex. 

Jamaika  by Markus Goetz 
Tirol Chocolate Purchased at IPP28 in Prague, from Wil Strijbos. 
Octix  Trigam 

Pairs of Prisms Ergatoudis IPP13 exchange 
Trevor Wood's Prism Cube  unknown craftsman Made from highly figured canarywood. 
3 Pyramid Cube by Philos 

The Jeu du Cube and L'Enervant puzzles are vintage French noncartesian cube dissections. (I believe Le Tracassier is also the same set of six pieces.) 

Obsivac Cube 1 
Obsivac Cube 3 
Naef Kniff by Manfred Zipfel and Cordula von Tettau (See Ishino's Kniff page.) Purchased at IPP28 in Prague. 



The Triangle Cube aka Pantene 
The 3456 Pythagoras Puzzle from Pentangle challenges you to use the nine pieces to form a set of three cubes 3x3x3, 4x4x4, and 5x5x5, then add them together and form one 6x6x6. 
Hexahedroom This very nice puzzle was made by Eric Fuller, from Ebony and Jatoba woods. Form a cube within the box by fitting the pieces in via the available holes. A cool solution. Based on an IPP25 exchange from Hirokazu Iwasawa. 

Olymp by JCC 
The Double Octagon Box from Bits & Pieces Same idea as the cereal box puzzles from Synergistics. 
peg square (not sure of name or manufacturer; it's not the Naef design) 

The Sticky Cube Designed by Bernhard Schweitzer A gift from Bernhard at IPP 29 in SF  thanks! 
This sixpiece puzzle is a 3D printed adaptation by George Bell, of Stewart Coffin's Peanut design (see the original in wood at PuzzleWorld, and at Scott T. Peterson's site). I ordered the 3 cm. version from George's Shapeways store, in Alumide material. (Photo by John Devost.)
Overall,
According to George Bell, the six pieces (or subsets of them) can form only a limited number of symmetric shapes
(but he doesn't know how many of each could actually be assembled,
since in some the pieces interfere with each other and won't slide together):
(1) 3ball: 21 flat triangle;
There are many more asymmetric shapes. 

Only 2 Sticks designed by Kofuh Satoh and made by Saul Bobroff Purchased at NYPP Feb. 2010 

Holzwurm (Product No. 6038), from Philos. Designed by Dieter Matthes. Form a 3x3x3 cube from 9 pieces having protrusions and hollows. Purchased at The Games People Play. 
TwistLDan, in Oak, Wenge, and Karin woods, designed by Takeyuki Endo. Purchased from the Karakuri Club. 
8Pd, in Oak, Angsana, and Karin woods, designed by Takeyuki Endo. Purchased from the Karakuri Club. 

One Four All & All Four One Made by and purchased from Mr. Puzzle Australia. Designed by Arcady Dyskin and Pantazis Houlis Entered in the IPP30 2010 Nob Yoshigahara Puzzle Design Competition, where it placed in the top ten. Arrange the four pieces (representing the three Musketeers plus d'Artagnan) in the frame so that they are selfsupporting in the frame  you must be able to handle the frame without the pieces falling out. The frame is made from Queensland Blackbean with Queensland Silver Ash joins. The pieces are made from Queensland Silver Ash, Papua New Guinean Rosewood, Western Australian Jarrah & Queensland Blackbean. 
Yubisaki Annai  Takeyuki Endo  IPP30 Fit the six 1x1x2 blocks into the cage. Five blocks each have a protrusion that will interfere with other blocks and the cage. 

A set of three Star Wars themed Pizza Hut (South American) promotional puzzles from 1997 
the Death Star (interlocking/assembly); Han Solo frozen in Carbonite (sliding piece); and R2D2 fixing C3PO (dexterity):

Promotional puzzle from IBM What solid shape will fit through each hole, completely filling the outline? 

TriBal Trifle, designed and exchanged at IPP32 by Rob Hegge, made by Formulor Assemble the pieces so that the triangular armature balances. 
Knobeltorte A puttogether puzzle in an egg. Layers of pieces with indents and knobs similar to the Prairie Dog Town puzzle. 

Full Bloom, designed by Ferdinand Lammertink, made and exchanged at IPP32 by George Miller Eight rings, each having two petals in various positions. Stack the rings so that no petals overlap. 
Jerrymander, designed and exchanged at IPP32 by Bill Cutler, made by Laser Perfect 
Washington DC Sightseeing, designed by Tania Gillen, made and exchanged at IPP32 by Marcel Gillen 

DC Tease, designed, made, and exchanged at IPP32 by James Kerley 
Tantalizing, designed, made, and exchanged at IPP32 by YeeDian Lee 
Shameful Congressional Gridlock, designed and made by Vaclav Obsivac, exchanged at IPP32 by Patrick Major 



GeoBrix  at first sight seems to be a standard 2D tray packing puzzle.
There are thirteen substantialsized pieces  each a black solid planar polycube with one colored face. They include some tetracubes, pentacubes, a hexacube, and a septacube. However, not only is there the expected challenge to fit the pieces back into the square 8x8 tray (for which there are at least 18 solutions) but an included booklet gives 20 different tangramlike silhouettes to be built from the pieces. And finally, one can build a 4x4x4 solid cube from the pieces. Lots of replay value here. Solutions are included.

Puzzle finger rings (Wikipedia article) made from several interlaced bands have been crafted by artisans from many cultures, and date back many years. The Puzzle Ring Store has a lot of info and a solution library.
This 4band puzzle ring was included in the "De Luxe Puzzle Chest" No. 3006 from F.A.O. Schwartz. It's the Extraordinary Ring Puzzle No. 3522 by Shackman. Made in Japan. 
This 6band puzzle ring was designed by Bram Cohen. It's 3D printed. I bought it from Bram at IPP 29 in SF. 
Here is a 7band puzzle ring I got in an auction lot. 
Holistic Ring, designed and exchanged at IPP32 by Bram Cohen, made by Oskar van Deventer & Shapeways 
An outfit called "Synergistics Research Corp." (New York, New York 10011), which evidently no longer exists, made several plastic assembly/packing puzzles years ago. I have not found an exhaustive list, but they include:
Here is an analysis I did of the Synergistics LifeSavers puzzle. I have found that all "flavors" use the same set of piece shapes. Each consists of 12 tori having combinations of pegs and holes. The tori stack together and fit into a cylindrical container approximately 55mm in diameter by 120mm high.
Each torus has a central hole immaterial to the solution. Each of the four cardinal positions (i.e north, south, east, and west) on its two faces may have one of the following features:
In total, there are 22 holes and 22 peglengths. For a puzzle of this type to have a solution, the total holes must equal or exceed the total peglengths.
This puzzle can be solved using PuzzleSolver 3D, if it is mapped to an analogue composed of unit cubes. My mapping is straightforward but imperfect as it will allow "illegal" solutions  fortunately the first solution produced is acceptable.
My mapping is as follows: rotate each torus depicted by 45 degrees clockwise. Use a 3x3 grid of cubes to model the torus and any holes  delete a corner cube corresponding to any hole. Leave the center cube filled in, to ensure the piece remains contiguous as required by PuzzleSolver. Add a cube extending outwards for a peg, or two stacked for a doublelength peg, at the appropriate corner positions on either side. The target volume is 3x3x12.
The diagram shows the disks, and the mapping of each disk to cubes. Two pieces are duplicated.
Solution number 1 is: 5, 2, 12, 9, 8, 6, 3, 1, 10, 11, 7, 4.
And here is an image of the solution #1, clipped from Puzzlesolver 3D:
Synergistics isn't the only firm that made puzzles in the shape of food items. Here are some additional examples...
I had a Parker Brothers' "Phony Baloney" when I was a kid  it disappeared but I found one in auction. 
This miniature version of Phony Baloney was a cerealbox prize. 
Here's one I found called the Banana Split, by Lakeside. 
Here is another Lakeside puzzle with a food theme  the Apple. Assemble the eight slices around the core so that the two "worms" can be inserted through the core to hold the puzzle together. The pieces have holes at 14 different heights, only two of which will line up with corresponding holes in the core. There are only two pairs of slices having corealigned holes. Not difficult, but cute. 
Prankfurter  Reiss 
Burger Thing  Reiss 
Here is a puzzle chocolate bar, the "Puzzle Bar" from Pentangle. 
Another hamburger puzzle, made in China. 
Here are Peter Piper's Fickle Pickles, a tenpiece packing puzzle. Made in Hong Kong, copyright 1973 Steven Mfg. Co. Discussed in Slocum and Botermans' The Book of Ingenious and Diabolical Puzzles on pp9091. (Click the image to see the solution, cheater.) 