a1 b1 c1 d1 e1 f1
a2 b2 c2 d2 e2 f2
a3 b3 c3 d3 e3 f3
a4 b4 c4 d4 e4 f4
a5 b5 c5 d5 e5 f5
a6 b6 c6 d6 e6 f6
A B A A B A
B C B B C B
A B A A B A
A B A A B A
B C B B C B
A B A A B A
Standard 7x7 Notation Hole Classification
(color coding used below).
(0,0) hole in bold.
6x6 Square 36-Hole 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 Comment
1 (0,0) c3 (0,0) c3 15 (S) 10 6 4 6 2 Corner finish possible
2 (3,0) c6 (0,0) c3 15 7 8 8 6 3 Corner finish not possible (in 15 moves)
3 (3,3) f6 (0,0) c3 16 (S) 1085 9 8 3 22 Corner finish possible
4 (3,0) c1 (3,0) c1 16 1732 10 10 3 61 Corner finish possible
5 (0,0) c4 (3,0) c1 15 62 8 7 4 6 Corner finish possible
6 (0,3) f4 (3,0) c1 15 62 8 7 5 6 Corner finish not possible (in 15 moves)
7 (3,3) f1 (3,0) c1 16 1346 9 8 3 14 Corner finish possible (like c1 to c1 after first move)
8 (3,3) a1 (3,3) a1 16 (S) 215 9 9 5 17 Corner finish possible
9 (0,0) d4 (3,3) a1 15 (S) 120 8 8 5 9 Corner finish possible
10 (3,0) d1 (3,3) a1 15 4 6 6 6 1 Corner finish not possible (in 15 moves)
11 (0,2) c2 (0,2) c2 15 70 7 3 4 1 Corner finish possible
12 (3,2) f2 (0,2) c2 15 70 9 9 4 11 Corner finish not possible (in 15 moves)
13 (0,-1) c5 (0,2) c2 15 110 8 7 4 5 Corner finish possible (like c2 to c2 after first move)
14 (3,-1) f5 (0,2) c2 15 70 9 9 4 11 Corner finish not possible (in 15 moves)
15 (3,2) a2 (3,2) a2 15 14 9 9 6 4 Corner finish not possible (in 15 moves)
16 (0,2) d2 (3,2) a2 15 161 8 8 4 13 Corner finish possible
17 (0,-1) d5 (3,2) a2 15 200 8 8 4 15 Corner finish possible (like d2 to a2 after first move)
18 (3,-1) a5 (3,2) a2 15 14 9 9 6 4 Corner finish not possible (in 15 moves)
19 (2,2) b2 (2,2) b2 15 (S) 136 6 6 4 4 Corner finish possible
20 (2,-1) e2 (2,2) b2 15 308 8 8 4 8 Corner finish possible
21 (-1,-1) e5 (2,2) b2 15 (S) 172 8 8 4 12 Corner finish possible
                       
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)
Corner finish A corner finish is when the last 4 moves originate from the 4 corners
(S) Problem is symmetric, multiple solutions counted as one
Note that solution diagrams are given for Vacate/Finish At in Cartesian Coordinates.
   To match locations shown in standard notation, reflection and/or reflection is generally needed.
Solution differences can be very subtle.

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