a1
a2 b2
a3 b3 c3
a4 b4 c4 d4
a5 b5 c5 d5 e5
a6 b6 c6 d6 e6 f6
a7 b7 c7 d7 e7 f7 g7
Square lattice representation and board notation.
(0,0) hole in bold.
Normal representation with board notation.
This is NOT a null class board, and no single vacancy to single survivor problem is solvable that begins or finishes at the center c5 or any corner. We can vacate any red hole, and finish in any green hole. All such problems constitute every possible single vacancy to single survivor problem (solvable by considering the fundamental classes).
28 Hole Triangular Board [Preliminary results]
Single Vacancy to Single Survivor Problems
# Vacate Finish at Length of Shortest Solution Number of Solutions Longest Sweep Longest Finishing Sweep Shortest Longest Sweep Number of Final Moves #(Longest, Second longest, Final) [Comment]
1 (0,-1) a2 (1,-1) b2 12 25 5 5 5 1 8(5,5,5), 17(5,4,5)
2 (1,-6) b7 (1,-1) b2 12 6 6 5 5 2 2(6,5,5), 4(5,4,5)
3 (5,-5) f6 (1,-1) b2 13 938 9 7 3 37 3(9,2,2), 1(8,3,3), 2(8,3,2), 8(8,2,2), 9(7,4,7), 3(7,4,4), 3(7,4,2), etc.
4 (0,-4) a5 (1,-1) b2 12            
5 (4,-6) e7 (1,-1) b2 12            
6 (2,-2) c3 (1,-1) b2 12            
7 (1,-3) b4 (1,-1) b2 12            
8 (3,-4) d5 (1,-1) b2 12            
9 (2,-5) c6 (1,-1) b2 13            
10 (0,-1) a2 (0,-2) a3 12            
11 (1,-6) b7 (0,-2) a3 12            
12 (5,-5) f6 (0,-2) a3 12            
13 (0,-4) a5 (0,-2) a3 12 274 11 11 4 57 1(11,2,11), 2(10,3,10), 8(9,3,9), 13(8,4,8), 11(8,3,8), 2(7,6,7), 7(7,5,7), etc.
14 (4,-6) e7 (0,-2) a3 12 311 9 9 4 47 2(9,4,9), 1(9,3,9), 1(9,2,9), 2(8,4,8), 1(7,5,7), 17(7,4,7), 4(7,4,1),
15 (2,-2) c3 (0,-2) a3 12 419 10 10 4 54 1(10,3,10), 4(9,3,9), 7(8,4,8), 2(8,3,1), 2(7,6,6), 1(7,5,7), 1(7,5,2), etc.
16 (1,-3) b4 (0,-2) a3 12            
17 (3,-4) d5 (0,-2) a3 12            
18 (2,-5) c6 (0,-2) a3 12            
19 (0,-1) a2 (2,-3) c4 13            
20 (1,-6) b7 (2,-3) c4 13            
21 (5,-5) f6 (2,-3) c4 13            
22 (0,-4) a5 (2,-3) c4 12            
23 (4,-6) e7 (2,-3) c4 12            
24 (2,-2) c3 (2,-3) c4 12 13 7 5 4 3 1(7,6,3), 2(6,5,5), 2(5,4,4), 8(4,4,4)
25 (1,-3) b4 (2,-3) c4 13 1000 7 7 3 26 4(7,3,7), 8(7,3,3), 2(7,3,2), 1(6,6,6), 8(6,5,6), 2(6,5,4), 24(6,4,6), etc.
26 (3,-4) d5 (2,-3) c4 13            
27 (2,-5) c6 (2,-3) c4 13            
          Total: 2986          
Column Definitions:
Length of Shortest Solution This is the length of the shortest solution to this problem, minimizing total moves
Number of Solutions This is the number of unique solution sequences, irregardless of move order and symmetry
Longest Sweep This is the longest sweep possible in any minimal length solution [link to solution]
Longest Finishing Sweep This is the longest sweep in the final move of any minimal length solution [link]
Shortest Longest Sweep There is no minimal length solution where all sweeps are shorter than this number [link]
Number of Final Moves This is the number of different finishing moves (up to symmetry)
#(Longest, Second Longest, Eg. 12(8,7,2) indicates there are 12 solutions with different move sequences, where
, Final) the longest sweep is 8, the second longest sweep is 7, and the final sweep is 2
(S) Problem is symmetric, multiple solutions counted as one
Solution differences can be very subtle.
Download a zip file with all XXXX solutions

Triangular Peg Solitaire Main Page