Sliding Block Puzzles / Sliding Piece Puzzles


The puzzles in this section have pieces that slide, without lifting or jumping, from one position to another, and a space into which to slide the pieces.

This definition is from the foremost book about this category of puzzle, Sliding Piece Puzzles by L.E. (Edward) Hordern, which was published in 1986 by Oxford University Press as part of the Recreations in Mathematics series edited by David Singmaster. The book describes more than 270 sliding piece puzzles (also known as sliding block puzzles) and provides solutions.

(Actually, though, some modern "sliding piece" puzzles permit lifting the pieces. I'll include them in section F.)

The Cleverwood website has an informative excerpt from a precursor work by Hordern.

You can try some sliding block puzzles on-line at Nick Baxter's site hosted by John Rausch, including many designed by Minoru Abe and Serhiy Grabarchuk. You can also play Java versions on-line at, a German site. Try the Bulbous Blob online at Puzzlebeast. See this article by Ed Pegg, Jr. on sliding-block puzzles for an excellent survey. Ed discusses the Quzzle (which can be emulated using the Dad's Puzzle pieces). See Taniguchi's Programs page for a solver program.

In Sliding Piece Puzzles, Hordern defines four categories:
  1. Sliding block puzzles (subgroups A through G) - in which each piece can move independently of the others
  2. Soko (warehouse) puzzles (H1-H10) - in which one piece must push all the others
  3. Railway shunting puzzles (J1-J13) - in which one or two pieces must push or pull all the others
  4. Sliding puzzles with plungers or levers - in which pieces move in groups
The first category is further subdivided into the following subgroups, which Hordern labels A through G:
  • A1-A10 - Random arrangement sliding block puzzles
  • B1-B60 - Sliding block puzzles with uniform pieces
  • C1-C76 - Sliding block puzzles with rectangular pieces
  • D1-D50 - Sliding block puzzles with non-convex pieces (i.e. L-shaped or T-shaped pieces)
  • E1-E35 - Restricted-route sliding block puzzles (e.g. Perplexity and Rush Hour)
  • F1-F13 - Sliding block puzzles with special shaped pieces or where rotation is allowed
  • G1-G5 - Three-dimensional sliding block puzzles

In this section I cover examples of most of the above groups. I focus on those puzzles in my collection, and show a few others for reference. The Soko-type puzzles are typically presented as electronic games or computer software programs rather than physical mechanical puzzles, and I do not cover them. The book does not cover the last category (4), other than to show a color plate of some example puzzles, including The Ten Billion Barrel and Trillion, and is very light on (G). Three-dimensional sliding piece puzzles are a huge category and I cover them on my Rearrangement page.

The most well-known sliding-block puzzle is the "Fifteen" (or "15") puzzle. Over a century before Rubik's Cube, in 1880, the Fifteen puzzle started one of the first puzzle crazes to occupy America and Europe. The Fifteen puzzle was first marketed in Boston by Matthias J. Rice, who called it "The Gem Puzzle." It was a tray containing fifteen numbered wooden blocks. The box top provided simple instructions: "Place the blocks in the box irregularly, then move until in regular order." The ambiguity of these instructions contributed to the popularity of the puzzle. I found a copy but I am missing the "14" piece.

It was eventually proved that half the random arrangements can be solved, while the other half are impossible. We now distinguish the solvable from the unsolvable arrangements by checking their "parity" - which amounts to the number of pairs which must be swapped to restore regular order. If the parity proves even, the position is solvable - if odd, unsolvable. This did not prevent people from claiming to have solved impossible arrangements. Most often their "solution" entailed some way of re-defining the goal state - for instance placing the empty space elsewhere than at the lower right, ordering the numbers in some way other than left to right in rows down the tray, or making use of a rotation of the tray itself (thusly leaving the figures not right-side up, or employing round tiles so as to be able to re-right them afterwards).

Jerry Slocum and Dic Sonneveld put out a book on the history of the 15 puzzle. In the book, they reveal that although Sam Loyd claimed and often got inappropriate credit for its invention, the actual inventor was Noyes Chapman, a postmaster in Canastota, New York, who applied for a patent in 1880. The patent was denied, perhaps because the 15 Puzzle was too similar to 207124 - Kinsey 1878, which specified the tongue-and-groove arrangement now commonly used for holding the tiles in the tray. Sam Loyd really shouldn't even be credited with popularizing the impossible challenge called "14-15" in which the starting position has only the 14 and 15 tiles swapped. The probable impossibility of that challenge was already appreciated back during the original craze. Since this position has odd parity, it cannot be solved. Loyd must have felt secure in offering a $1000 prize for a solution!

Hordern categorizes the Fifteen puzzle (along with the 14-15) as B10, rather than in the A group - probably because only a specific subset of starting positions is solvable. Hordern's first puzzle in the A group, A1, is RATE YOUR MIND PAL. It can always be solved, regardless of the initial position of the blocks. Bearing in mind the parity issue, can you figure out why?

In his 1942 book 100 Puzzles - How to Make and Solve Them,
Anthony Filipiak describes and provides solutions for ten "shifting block" puzzles,
most of which are covered by Hordern.

19 Block - H.C71

9 Block - H.C19 Dad's Puzzle

5 Block - H.B1 - Sam Loyd's The Moving Day Puzzle

11 Block - H.C52

Bull's Eye (11 blocks) - H.B23 ZOT

George Washington's Career (15 blocks) - H.C67

10 Block - H.C17 Schweig's Trans-Atlantic

15 Block or 1-2-3 - H.C72

Rectangle - H.D1-3 Ma's Puzzle

27 Block

(A) Random Arrangement


Franklyn's Tobacco Puzzle
When solved, it reads "Smoke Franklyns Fine Shagg It Is Good."


United States
I don't have it.
Start with the blocks in random positions, finish as shown. Black squares are impassable.

Question du Jour
(aka La Grande Question or the Columbia Puzzle)

Ten Little N****r Boys
See U.S. patent 602735 - Donaldson 1898.
Also see 437932 - McGrath 1890.
(I don't have this.)

Le Moulin Rouge

Au revoir, Do svidania
(I don't have this.)

Latin Square variants
such as the Roalex Psycho Numbers
(I don't have this.)

Four Square (aka Court Card by Fairylite)
Objective is a Graeco-Latin Square.
See U.S. patent 433444 - Brown 1890.
(I don't have this.)

Another Latin square.

The White Eagle Mobil Gas puzzle
Shuffle the 19 cards, place in four horizontal rows of five cards each, letter side up, leaving one open space (at lower right). Slide cards left/right & up/down, using the open space, until they read "White Eagle Mobil Gas" followed by the symbol card and the space.

The 14 Puzzle - Milton Bradley
Drop the pieces on the board randomly - place each on its nearest space.
Find 14 and put it in the center and don't move it until the end.
Using the single open space, move the pieces along the dotted lines only,
until each piece rests on the corresponding numbered space. Move 14 into place last.

(B) Uniform Pieces

B   T

The Moving Day Puzzle
eq. to the 5 Block Puzzle in Filipiak
Five square (1x1) blocks in a 2x3 tray. Exchange B and I in the fewest moves. I don't know if this was ever produced as a physical puzzle - I don't have it and I don't have a photo, but it is easy to emulate (I made one from Lego) and I think it is a great little puzzle to try. See the Moving Day Puzzle in an online version of Sam Loyd's Cyclopedia at Ed Pegg's site. Play it online at or at Nick Baxter's site.

B5 (B4 thru B8)
Eight Block Puzzle (various start and end conditions)
A 3x3 grid with one space and eight uniform blocks. Many variations exist, including this Sun Face.
Play B6, Dudeney's Letter Block, online at or Nick Baxter's site.

The Flanders Wheel
From Puzzles and Curious Problems by H. Dudeney ca.1917
I don't have it or a photo.
Move the pieces along the lines from spot to spot starting with the arrangement shown, so FLANDERS can be read clockwise beginning with the F at 12 o'clock.

The Fifteen Puzzle
There have been countless variations produced, including an early wooden version from the Embossing Co. of NY, a nice metal version from Binary Arts and a cheap plastic smiley-face version.
B11-B15 are variations, some to form magic squares rather than order the numbers.
16 15 14 13
12 11 10 9
8 7 6 5
4 3 2 1

1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16

Tit-Bits Teaser No. 6 (1932)
A variant of the 15 Puzzle. Start with the first arrangement, remove the 16, and slide the blocks to get to the second arrangement.

The Maltese Cross Puzzle
Advertising item for Hires Root Beer
(I don't have this.)
U.S. Patent D0019756 - Spayd 1890
I can't find this in Hordern.

Kenreign Rain Coat New Puzzle Game

Prosperity Puzzle

The Improved 15 (Star) Puzzle

"Blocks of Five" or the Administration Puzzle
Blaine is in. How can Harrison get him out?
(I don't have this - shown for reference.)
To start, put Harrison around the outside instead of JG Blaine - end as shown.
The center (representing the White House) is the empty square.
The CABINET$ will be moved as needed during solving but must start and end arranged as shown.
2 3 4
5 6 7
8 9  

The Fifteen Puzzle (variation from Wit Sharpeners 1944)
I don't have it or a photo.
Slide the numbers to create a magic square where all rows, columns, and the two main diagonals add to 15.

Panama Canal
I don't have it. Play it online at or at Nick Baxter's site.

Good Luck
B19: Exchange rows 1 and 2 intact.
B20: Move row 1 to bottom, all rows end intact.

Capturing the Kaiser / Tit-Bits New Game
1914-18, 1930s
I don't have it or a photo.
Surround Kaiser Wilhelm, Von Tirpitz, the Crown Prince, and Count Zeppelin with soldiers.
Could this be the elusive Tit-Bits Teaser No. 3?

B24 is a variant called "ZOX" where the T is replaced by an X. In ZOX, the Z and X must end up in the same relative positions as at the start. This will require some lateral thinking!
B25 is a further variation, by N. Takashima.

Dormitory Dash - Peterson Games 1975


The Parking Lot Parable
1971 Products of the Behavioral Sciences, Inc.
Palo Alto CA
Start with the colored tiles as shown at left (white is space); end with no two tiles of the same color touching. The instructions say 24 moves; Hordern says 20 moves.

Gordon Bros. 1974
Shifty is equal to The Parking Lot Parable but poses additional challenges using the same pieces.
1 2 3
4 5 6

A Motor-Car Problem
Dudeney 1903
I don't have it or a photo.
Image is of a Russian version called Logi Toli.
Exchange 1/4, 2/5, 3/6.
This is the "three-letter" version of B35.


Work or Golf
(aka A Motor Garage Puzzle)
Play online at or at Nick Baxter's site.
See B33,B34 for the "three-letter" version of this four-letter puzzle.
B36 extends both words to five letters, and adds another "siding" space opposite the existing one.
  2 3 4 5 6 7 8 9 1

Nine Men in a Trench
I don't have it or a photo. Play it online at or at Nick Baxter's site.

B38 is a 1984 version from Hong Kong, where pieces 2-5 are one color, 6-9 a second color, and 1 a third color. You are to move 1 to the left side and swap the other two colored groups. The pic is from Martin Watson's collection. I don't have this.

So Easy / Le Jeu des Quatre Coins

L'Evasion Difficile
(I have the plainer version.)
  M I N E  

Anagram Blocks
From "Sam Loyd and His Puzzles" 1928. Rearrange the letters to spell "MAID ENLY" in two rows. I don't have it or a photo.

Honor and Glory
(Black and White)
Play Black and White online at Nick Baxter's site.

Nutzy Numbers (aka Tantalising 7, Nutty Numbers)
See U.S. Patent 3148884 - Steinhardt Sept. 1964

The Time Puzzle by the Embossing Company of Albany NY.
See patent 1989411 - 1935

The New 15 Puzzle

I found a copy of the Idiot's Delight sliding piece puzzle issued by Roalex.
The goal is to move the pieces such that no color appears more than once in any row, column, or diagonal.
The space must end in a corner.

A vintage Spacenik from Roalex.

There are many very collectible vintage sliding piece puzzles issued by Roalex. Here is a composite of some of them. I don't really collect these, so I have only a few of them. They can be quite expensive - the "Astro Boy" sold for about $3000!

(C) Rectangular Pieces

After the Fifteen Puzzle, the next two most-sold sliding piece puzzles are probably Dad's Puzzle(r), and the L'Ane Rouge design. Both have been extensively copied; the former used often for advertising, and the latter appearing in many modern versions.

Many different challenges can be attempted using the 4x5 tray and the following set of pieces:

These items will allow one to try puzzles C15 through C45 inclusive. Not every puzzle uses all the pieces.

4x5 designs which require large numbers of moves to complete include Quzzle by Jim Lewis (84 moves), Quzzle-Killer by Bob Henderson and Gil Dogon (90 moves), and finally the Super-Century by Gil Dogon, which requires the largest number of moves (138) for a 4x5 tray using rectangular pieces.

  1 2 3
A B 4

U.S. Patent 516035 - H. Walton 1894
Exchange A and B.
I don't have it or a photo.

Get My Goat
(Should have one rectangular piece in upper right, else it becomes B23.)
U.S. Patent 1112746 - Wiley 1914
Play online at Nick Baxter's site.

Katch the Kaiser


Line Up the Quinties
R. W. Fatiguant, 1934
Move the faces to form a line where the flowers are. Play it online at Nick Baxter's site.

The Merry Widow
U.S. Patent 922002 - Koehler 1909
(I don't have this.)
Diagrams from patent -
start as on left with "The Merry Widow" spelled backwards - small letters read "Will she get him" - end as on right. Note blocks are not all same size.
Photos from actual puzzle - small letters are absent.

A Yank Thru the Lines
1942 WWII Slidem-Solitaire Puzzle
Electric Corporation of America, Chicago

Bombing Tokyo
1942 WWII Slidem-Solitaire Puzzle
Electric Corporation of America, Chicago

Tank Attack
1942 WWII Slidem-Solitaire Puzzle
Electric Corporation of America, Chicago

The Hard Time Map Puzzle
(I don't have this.)

1     A
2 3 4  
7 6
  8 9

The Infant's Hospital Puzzle
Chad Valley 1920
I don't have this.
Move A to the bottom right. The black area is impassable. There is a 1x3 gap and a 1x1 gap.

Moss' Puzzle
See U.S. Patent 668386 - Frank E. Moss 1901
I don't have it or a photo - Hordern is unsure of whether this was ever produced.
The sides labeled a,b,c, and d are different colors - rectangular pieces G,H,J, and I are correspondingly colored. Each starts across from its corresponding side and must end up as shown. The corner pieces C,D,E, and F are each bi-colored according to their home positions. They start out diagonally across from their homes. The two middle pieces L and N remain in the middle but their respective positions don't matter.

The 10 Block Puzzle (Filipiak), aka Traffic Cop Tangle. Also appeared as Schweig's Transatlantic Puzzle.
Play online at Nick Baxter's site.

This puzzle was included in the "Party Puzzle Box Supreme" compendium from George Schweig & Son of Philadelphia PA.

The Pennant Puzzle
aka Dad's Puzzle(r)
The Pennant Puzzle was copyrighted in 1909 by Lewis W. Hardy, who had filed another patent (1017752) in 1907 which was not granted until 1912.
The Humdinger, Leech, Moving, G.I. Nutcracker, Eskimo Pie, Comet, and Setko Block puzzles are the same.
(I don't have the Pennant or Eskimo Pie versions. The Pennant, as baseball memorabilia, sold for $475! Thanks to Jan de Geus for pointing it out.)
Play online at or Nick Baxter's site.

A vintage sliding piece puzzle advertising premium from the "Hartford Despatch & Warehouse Co."
It's called The Moving Puzzle, but this is a 5x6 version I haven't seen before.

Jusso Nine Block Puzzle

L'Ane Rouge (The Red Donkey)
Patented in England ( 411515) by J. H. Fleming in 1932.
I have several modern versions, including a white plastic L'Ane Rouge, Haba's Quo Vadis, The VIP puzzle by Funtime Gifts Ltd., Tryne's Hako, Square Root, Hix Brix, Mintman (Mintman solution here) , (aka Klotski), the Chessmen, and Skor Mor's Ego Buster. This is also known in China as the Hua Rong Dao (Huarong Path), based on an escape of the warlord Cao Cao. In Japan, it is known as "Daughter in the Box." Other versions include Psychoteaze (which I don't have), and Intreeg (1949).
Play online at or Nick Baxter's site.

Let Me Through

Khun Phan (or Khum Pan)

Panama Blockade
(I don't have this.)
U.S. Patent 1415625 - Bulister 1922
For some reason, Hordern omits Blockado.
It is played on a 4x6 tray and is similar to C50,51, and 52.
Acme Novelty Sales, 1928
Play it at or on Nick Baxter's site.

The Flying Puzzle, Ching Foo, Tit-Bits Teaser #2, Silver Label, King Coal
These use a 6x5 tray.
U.S. Patent 1663568 - Schneider 1928
Move the plane to the bottom right corner - 55 moves.

Tit-Bits Teaser #5 aka The Train Puzzle
uses a second 2x2 square piece

The Presidential Puzzle
Listed as and identical to the Century of Progress Puzzle (which I don't have).
Move either large square (your candidate) to the lower left corner (the White House).

George Washington Puzzle

The Sliding Block Puzzle by S.S. Adams
Play online at Nick Baxter's site.

Slide Awhile
Rochester Puzzle Co.
Listed as Model Garage/Spot Check/The Blockade Puzzle
Move A to the bottom center.
(I don't have this.)

Al Smith to the White House (1928?)
Read some biographical material about Al Smith at
Two sliding-piece puzzles from Popular Playthings - Sink or Swim, and Outta Gas:

A sliding piece puzzle by Pussycat picturing some elephants and featuring a couple of 1x2 pieces to complicate things.

(D) Non-Convex Pieces

Ma's Puzzle
U.S. Patent 1633397 - Diamond 1927
Play online at or Nick Baxter's site.

A vintage sliding piece puzzle advertising Silverthorn's of Orfordville, Wisconsin. This is an instance of the classic design Ma's Puzzle, and while the related Dad's Puzzle has been used extensively for advertising, this is the first time I have seen Ma's puzzle used.

The Football Puzzle
See U.S. Patent 771514 - Wehner 1904

Move the ball piece from the center to either top or bottom center.

The Traffic Jam Puzzle
U.S. Patent 1683014 - Babcock 1928
aka Tit-Bits Teaser No. 4
Play online at or Nick Baxter's site.

Block 10 - Minoru Abe
D24-D49 are designs by Minoru Abe. Try some at Nick Baxter's site.

This is The Slider Puzzle designed by Serhiy Grabarchuk and sold by Bits and Pieces. It is not in Hordern's book.
Play online at Nick Baxter's site.

"Dog & Balls" (IPP27) designed by "Mine" (Mineyuki Uyematsu).

Budget Crisis, designed by Dick Hess and Neil Bickford, made by Laser Lynne, exchanged at IPP32 by Dick Hess

Tit-Bits Teasers

George Newnes was a British publisher and politician who lived from 1851 to 1910. Newnes' interest in entertaining snippets of information was his inspiration for the weekly 16-page penny paper Tit-Bits, which he launched in Manchester England in 1881. Newnes publicized Tit-Bits with a series of contests and promotions - for instance, an insurance scheme where the survivors of any reader killed in a railway accident and found with a copy of Tit-Bits on the body would receive 100 pounds! By 1891 there had been 36 cases. Newnes went on to found the Strand, published from 1891 until 1950. For twenty years, Henry Ernest Dudeney, England's foremost creator of puzzles, had a column "Perplexities" in the Strand. The Strand also first published the Sherlock Holmes mystery series by Sir Arthur Conan Doyle.

Among the promotions associated with Tit-Bits magazine were a series of puzzles called "Tit-Bits Teasers."

Tit-Bits Teaser No. 1 (1927)
This is equivalent to the Pennant Puzzle, or Dad's Puzzle.

Tit-Bits Teaser No. 2 (1928)
This is equivalent to Ching Foo and the Flying Puzzle.
Tit-Bits Teaser No. 3 (1929?)
(I don't have this.)

Tit-Bits Teaser No. 4 (1930)
This is equivalent to the Traffic Jam Puzzle.

Tit-Bits Teaser No. 5 (1931)
aka The Train Puzzle
16 15 14 13
12 11 10 9
8 7 6 5
4 3 2 1

1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16

Tit-Bits Teaser No. 6 (1932)
A variant of the 15 Puzzle. Start with the first arrangement, remove the 16, and slide the blocks to get to the second arrangement.

(E) Restricted-Route

The Four Frogs (aka Four Knights)
I don't have it. This puzzle is a sliding version of a chess variant problem: on a 3x3 board, start with two white knights at the north-east and north-west squares and two black knights at the south-east and south-west squares. Exchange the black and white knights in seven legal knight's moves. Note that the center square is never used.


Several variations on this design exist. See U.S. Patent 642374 - Shaffer 1900.


The Panama puzzle, from 1915. Not in Hordern. Start at the left end of the puzzle - put the three A's in slots 1, 2, and 3, and the other letters in slots 4, 5, and 6. In three moves exactly, moving two at a time that are adjacent and keeping them adjacent, spell PANAMA with no embedded spaces.
Here are more versions of the E10/E11 Perplexity design:

1904 Louisiana Purchase Expo

Shackman Famous Number Puzzle

1915 Panama Canal Expo

E15 through E18 clearly presage what has become one of the best-selling puzzles of modern times; Binary Arts' Rush Hour. Move a specific vehicle out the lone exit in the border, first figuring out a way to clear the path of obstructing vehicles. A deck of cards gives progressively harder problems to set up and try. There are several expansion packs with new cards and a vehicle.
Pink and Blue by Nob Yoshigahara 1982
I don't have it or a photo.
Play online at Nick Baxter's site.
Play other Nob puzzles at Nick Baxter's site.


Richard Appel Inc. USA 1943
(I don't have this.)
Move the purple piece at the top left corner to the bottom right corner - but pieces of the same color may not ever touch sides.
Hordern says this can be done in 22 moves.

Fox and Geese
I don't have it or a photo.
Start with three white pieces (geese) on 1,2,3 and three black pieces (foxes) on 10,11,12. Exchange the black and white pieces moving only along lines and stopping only on circles. At no time except in passing can a fox and goose be at opposite ends of any line.

A New Counter Puzzle
From Amusements in Mathematics H. Dudeney 1917
I don't have it or a photo.
Start with white pieces on 1 and 2 and black pieces on 9 and 10. Exchange them moving only along lines and stopping on numbered spots. At no time except in passing can a black and white be on the same straight line.

Discussed by Manasse, Sleator, Wei, Baxter in Tribute to a Mathemagician 2005 - see Baxter's page devoted to Panex. Key distinction from Towers of Hanoi: pieces will not descend below their appointed height in stack - 10-high stacks require 31,537 moves (verified by Derek Kisman, who developed an efficient search algorithm).
Play Panex online here, or a simplified version at Cheesygames.
Kisman also found that the shortest solution for level 11 is 76,245 moves; level 12 is 184,191; and level 13 is 444,807.

The pieces interfere with some of their neighbors, preventing some movements.

The pieces interfere with some of their neighbors, preventing some movements.

Roadside Rescue - Thinkfun

Two Sliding Squares - Grabarchuk - from Bits & Pieces. The blue parts are attached to the tops of some of the silver pieces, and overhang some piece edges. Slide the pieces to form a large square with the blue parts. (This combines a sliding piece puzzle with a well-known square dissection.)

invented by Vesa Timonen and Timo Jokitalo
Tilt the board to slide green, but not the blue, pieces into the central hole. Every move must move all pieces in the tilt direction as far as each can go unobstructed. Fun!

Rudenko Mosaic
The New Door Puzzle
Slide the buttons using the central carousel, to transform the letters of "NEW DOOR" into 1 word. A nice metal implementation of a well-known anagram puzzle.
SPOILER ALERT: See U.S. Patent 1132430 issued to Brogan and Bruner on March 16, 1915.
My copy is missing one of the buttons (one of the 'O's).

Russian 4x4 puzzle

A while back there was a computer game called "The Seventh Guest" and a sequel called "The Eleventh Hour." Both were puzzle-based "adventure" games with a horror/suspense flavor. The Eleventh Hour contained a version of a classic puzzle challenge known by various names including the "Crazy Knights" and "Knights Exchange." Adventure games have contained many logic puzzles that yield to mathematical analysis.

Arabesk offers this version of Crazy Knights. (I don't have it.) The Knights Exchange is played on the irregular fragment of a chessboard shown here. For discussion, I have numbered the squares. The initial condition of the puzzle has white knights on squares 6 and 10, and black knights on 1 and 3, and your task is to interchange their positions using only legal knight's moves. This can be done in 40 moves.

|  1 |
|  2 |  5 |  8 | 10 |
|  3 |  6 |  9 |
|  4 |  7 |


To solve this puzzle, consider that it might be easier to analyze if you were able to look at it in a different (although isomorphic) way. Starting with the square designated 1, construct a graph where each node represents a square, and each edge between nodes represents a (reversible) knight's move between the corresponding squares. Arrange the graph as a simple unbalanced binary tree with 1 as the root.

Using the graph, you'll note that movement has been conceptually simplified, making the whole puzzle easier to comprehend and attack. Rather than hard-to-visualize knight's moves on the irregular chessboard fragment, you're now dealing with simple moves from node to node along the edges of a straightforward tree.

We've "reduced" the problem to a Perplexity-type puzzle - you can think of the nodes 10 through 5 as a straight track, having a single side branch or "parking space" at 3. You've got 2 white pieces and two black pieces and you've got to shuffle them past each other exploiting the single parking space at 3.

        /   \
     (6)    (8)
     /     /   \
  (10)   (3)   (7)


You may wish to attempt to deduce a winning sequence yourself now that you have a better representation of the puzzle with which to work (read on at the risk of spoiling whatever remains of the puzzle).

Here is a sequence of moves which accomplish the task. 'B' represents a black knight; 'W' a white knight. B@n means a black knight at square number 'n'. Two numbers separated by commas mean move whatever is on the square designated by the left hand number to the square designated by the right hand number.

If you count the commas (which are moves) you'll see there are 40. Also, note that we didn't need squares 4 and 5 at all.

To solve this puzzle, I've employed a strategy common in mathematics and operations research - when faced with a problem, try to find an isomorphism with another type of problem for which a solution can be more easily found. I'll readily admit that this strategy cannot be used on every puzzle, but I thought this was a great example.


(F) Special Pieces / Rotation Allowed

Here is an interesting series designed by Hirokazu Iwasawa aka "Iwahiro."
Rectangular Jam, Triangle Jam, Rightangle Jam, Pentangular Jam, Hexangular Jam, and 5 Yen in a Jam (IPP28)
Get the highlighted block out through a slot in the south wall. Unusual because you may rotate the pieces flat in the tray.

Straight Arrow, from Thinkfun, is a nice, portable, inexpensive copy of Iwahiro's Rectangular Jam.

The Combination Lock
Mfd. by the Combination Novelty Co.
See U.S. Patent 560197 - Dow 1896.

Drop Out
Designed by Stewart Coffin (#202)
IPP27 exchange puzzle of Henry Strout
Four 1x2 blocks and one 1x1 block are contained in a 3x4 tray with a transparent cover which has a hole in one end - the bottom of the tray has a hole in the other end. Drop in a magnetic disk then by shifting pieces, get it out the opposite hole. Requires 26 moves. If the disk is dropped in again with the blocks as positioned after the solve, there is no solution! It takes 8 moves to restore the blocks to a solvable state.

The Flying Block (or Jumping Block) puzzle designed by Dries de Clercq.
A gift from Dirk Weber at IPP28 in Prague. Thanks again, Dirk!
Sliding, jumping, and rotation of pieces are allowed, but only one piece at a time. Mr. Puzzle Australia produced one.

Flying Block II
IPP 29 in SF

Flying Block III
David at Eureka recommended the Dig It! puzzle produced by Foxmind.
It is designed by Alex Polonsky. There are 50 challenges in four increasing levels of difficulty. In each, you must move a set of pieces in succession until a "bone" piece is fully revealed.

This reminds me of de Clercq's Flying Block puzzles.

Twist-'N'-Slide Truck

Unusual Features

This section contains sliding piece puzzles having unusual features.

This is an interesting version of the sliding block theme called Color Magic. I bought it at Games People Play. It is from the Metropolitan Museum of Art. Begin with primary colors. Slide the fifteen tinted translucent tiles in order to produce the secondary colors. The color of a tile combines with the color of the square printed beneath it on the base.

Janus - by Frank Potts
(I don't have this.)
The idea here is to solve a kind of 15 puzzle, but the twist is that each number is represented in stylized segmented form and has been decomposed into two sets of segments, each of which is on a separate transparent layer. Essentially you need to solve two 15 puzzles simultaneously so that the transparent tiles combine properly to re-form the numbers in order. Some thought went into how to best decompose the numbers into two separate layers, to allow one proper solution. Another twist is to present a 15-14 version that can be solved with a parity trick.
Frank says he made only two to enter in the IPP 2005 design competition - the photo is from the design competition page on John Rausch's site.
Play Janus online at Frank's website.

Puzzle Impossible, from Hanayama. This is an unusual sliding piece puzzle - marks on the transparent pieces combine with marks on the tray to form digits. Purchased at Eureka.

The Svetnashki is a sliding piece puzzle design from Russia, based on polarized light - It comes in two sizes: 7 cm. and 10 cm.

Produced by Smart Games, designed by Raf Peeters.

Chicken Shuffle
Produced by Smart Games, designed by Raf Peeters.

Produced by Smart Games, Anti Virus is the production edition of Bulbous Blob designed by Oskar van Deventer and James W. Stephens - you can see it and play a few levels at the Puzzlebeast website. It's like a crab-wise variant of Rush Hour, but with a nice added level of complexity due to the richer movement possibilities.

Produced by Smart Games, designed by Raf Peeters.
Also similar to Rush Hour. A very slick design - the problem initial position card is visible when you look straight down through the "water." A set of passengers need to be rescued by a set of lifeboats, which can move forward, backwards, or sideways unless blocked. Passengers scramble into free seats as soon as possible. A full boat must remain stationary (and therefore impedes the movement of other boats).

Perplexing Palace, designed, made, and exchanged at IPP32 by James Dalgety

Yusei, designed, made, and exchanged at IPP32 by Takeyuki Endo
Slide the pieces in the frame to form a star. The top point of the star can stick out of the frame.

Minoru Abe's Tricky?

Zen Benders Dragon

Arrow Blocks - designed by Goh Pit Khiam, made by Tom Lensch.
The frame is Indian Rosewood. The pieces are Maple and the arrows are Yellowheart and Brazilian Blackwood. A nice substantial size - the tray is 7" x 5.5" x 1" thick. The pieces are 1.5" squares.
Entered in the 2012 IPP Design Competition. Tom's creations are always a joy to behold and to play with, and this is no exception. And this design from Goh Pit Khiam is no less tricky than his others. Named one of the top puzzle finds of 2012 at a recent gathering of puzzlers.
Only six blocks - all distinct - each showing part of a yellow or brown arrow, and each having various internal flanges that interact both with other pieces as well as the inside of the tray walls. Starting with the pieces in the position shown, restore both arrows. A sequential movement puzzle that appears at first glance to be a simple sliding piece problem. However, astute observers will note the internal flanges that are blocking the last piece, the yellow arrowhead, from being placed in the tray. It won't be as easy as it might seem!
Employing internal flange concepts similar to the Tom's Square Dance and "Little Window" from Tom Jolly.

This is Qubigon, a new release from Brainwright. It is a sliding-piece puzzle using magnetic pieces on the surface of an icosahedron. The pieces are numbered 1 through 18 and colored either white, blue, or purple to aid in recognition. Each piece has a correspondingly numbered and colored triangle on the face of the icosahedron. There are also two yellow faces, and one yellow "Genius" piece. The normal puzzle is to remove the yellow marker and scramble all the other pieces around the icosahedron, then by using the two empty faces, slide the pieces to return them to their home faces. The magnetic tiles adhere nicely and slide across the edges from face to face with a satisfying click. For added difficulty, you can add back in the yellow piece and end with it on one of the yellow faces.

The Mirage Puzzle designed by Serhiy Grabarchuk in 1992
It is described in his book "Neo Sliding Block Puzzles"
The acrylic enclosure sandwiches two layers of sliding tiles, a fixed
island in the center, and a single-tile single-layer space. Using the space,
slide the tiles between start and goal configs described on the website (cw b,1,2,3,4,5,6,7) -> all 7s.

Soko or Warehouse Puzzles

Thinkfun has issued a soko-type puzzle called Treasure Quest

Shunting Puzzles

Railroad Shunting Puzzles (or switching puzzles) have been around since the late 1800s - according to Slocum and Botermans on page 106 of their "New Book of Puzzles," the first U.S. patent was issued to Pryse Protheroe in 1885. I did some sleuthing and the results are summarised in the table below.

You, too, can search the U.S. Patent database. The CCL for "shifting movement" puzzles of this type is 273/153s. Last time I checked, there were 533 hits spanning many different kinds of puzzles. NOTE: to view the patents, you'll need a TIFF plug-in for your browser.

Pryse Protheroe 1885 332211
Employs a turntable.

Arthur G. Farwell 30 Sep. 1890 437186
W.W. Rouse Ball in "Mathematical Recreations and Essays" p.114 (11th Ed. 6th printing 1973, orig. pub. 1892), says he bought a shunting puzzle "some years ago" called the Great Northern Puzzle. The configuration illustrated in the book resembles Farwell's. A similar configuration is shown in the Wagon Works puzzle described on "The Ultimate Puzzle Site: Logical Puzzles." (Warning: Pop-Ups on the main page.)

Charles W. Lurtey 9 Dec. 1890 442445 - this looks like the "Engineer's and Switchman's Puzzle" shown below. See also Burger 1933 below.

James E. Jackson 1891 449881 - 3 cars in the triangle, loco to the right

John Alfred Allen 1892 482957

John M. Rodgers 1901 688339

Frank Lisle Napier 1902 703076 - this is almost certainly the Railroad Pass shown below, by the Napier Mfg. Co.

Martin H. Anderson 1903
Street Car Puzzle

Edward S. Mowry 1903
743015 - W.W. Rouse Ball on p.115 calls this the Chifu-Chemulpo Puzzle, on sale in the streets in 1905. The main line can hold only 8 cars and the spur only 4. To start, 8 numbered cars reside on the main line in order and the engine on the spur. The object is to reverse the order of the cars.
See the similar "Good Luck" horseshoe-shaped puzzle shown below.

Henry Keeler Feb. 1904 750862

Orril L. Hubbard Mar. 1904 753266 - using turntable

Livingston B. Pennell Feb 1905 783589

Charles E. Harris Nov 1905 804314

W.E. McGraw & A.M Goodale 1906 822862 - 4 cars in triangle

Harry G. Webster 1907 856749 - switch positions on S-shaped track

John J. Barnes Dec. 1907 874726 - several puzzles using a comprehensive track layout

Solon S. Cahill 1908 878187 - also shown here: Grantham vs. Boston - a simple passing problem with one short siding (aka "blind spur")

John W. Clark 1908 898321

Charles M. Conley 1912 1018879

Thomas F. Young 1916 1174219

John W. Braunschweiler 1918 1275210

John Vandever Wells 1921 1377039 - 2 puzzles, unique switches

Bruno von Bueltzingsloewen 1925 1560921

Maximilian E. Pesnel 1928 1673705

Clarence W. Burger 1933 1920291 - This looks like the Engineer's and Switchman's Puzzle shown below, but shows eight pieces while the actual puzzle has an engine and five numbered cars.

Leo J. White 1964 3127175

William A. Sternad 1973 3767202

Here are some examples of railroad shunting puzzles which have been sold as mechanical puzzles.

Engineer's and Switchman's Puzzle
see Slocum and Botermans' "Puzzles Old & New" p.10

Good Luck - Saleable Products
(Hordern J7)

A wooden repro of a Protheroe-type turntable

Metro by Binary Arts

Napier - Railroad Pass
(I don't have this.)

(Hordern E7)

Here is a copy of the Great Northern Puzzle. (I don't have it.)

Train in Line - Bits & Pieces
A nice wooden railroad shunting puzzle with 5 numbered cars.

Here is my solution to the Wagon Works shunting puzzle. Start in the upper left and proceed left to right row by row down the page, ending in the lower right.

Shunting puzzles can be built in model railroad layouts, but they are usually considerably more complex than the mechanical puzzles described here. Model railroaders try to create more realistic scenarios using several long sidings, runarounds, and trailing and facing switches. The operations at various industrial locations that require lots of shifting of cars and loads, such as mines, paper mills, breweries, or cement plants, can serve as the objective. Real railroads (known as prototypes) strive to avoid the switchback maneuver common to these puzzles, and operators prefer to do a "grand pull."

Adrian Wymann has a nice site on railroad shunting puzzles. Carl Arendt's site shows many layouts including puzzles (see Micro Layout Design Gallery, Scrapbook page 45).

Here are some model railroad puzzle layouts: