| 41-Hole Diamond Board |
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| Single Vacancy
to Single Survivor Problems |
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| # |
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 |
(-1,3) |
d2 |
(1,3) |
f2 |
26 |
30 |
9 |
1 |
5 |
1 |
2(9,3,1), 2(7,3,1), 10(6,5,1), 10(6,3,1), 6(5,5,1) |
| 2 |
(2,0) |
g5 |
(1,3) |
f2 |
26 |
26 |
9 |
1 |
5 |
1 |
2(9,3,1), 5(7,3,1), 5(6,5,1), 1(6,4,1), 9(6,3,1),
2(5,5,1), 1(5,4,1), 1(5,3,1) |
| 3 |
(-1,3) |
d2 |
(-2,0) |
c5 |
26 |
61 |
7 |
1 |
4 |
2 |
1(7,5,1), 4(6,6,1), 10(6,5,1), 5(6,4,1), 14(6,3,1),
4(5,5,1), 18(5,4,1), 5(4,4,1) |
| 4 |
(2,0) |
g5 |
(-2,0) |
c5 |
26 (S) |
131 |
7 |
1 |
4 |
3 |
2(7,5,1), 15(7,4,1), 10(7,3,1), 29(6,5,1), 19(6,4,1),
6(6,3,1), 17(5,5,1), 19(5,4,1), 12(5,3,1), 2(4,4,1) |
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Total: |
248 |
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| Column
Definitions: |
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| Length of
Shortest Solution |
This is the length of the shortest solution to
this problem, minimizing total moves |
| Number of
Solutions |
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This is the number of unique solution sequences,
irregardless of move order and symmetry |
| Longest Sweep |
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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 |
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, 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 |
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| Note that
solution diagrams are given for Vacate/Finish At in Cartesian Coordinates. |
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| Solution
differences can be very subtle. |
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| Download a text file with all 248
solutions |
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