| French 37-Hole 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 Sweep, Final
Sweep) [Comment] |
| 1 |
(-1,3) |
c1 |
(1,3) |
e1 |
20 |
243 |
8 |
4 |
5 |
7 |
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| 2 |
(-1,3) |
c1 |
(-2,0) |
b4 |
20 |
35 |
7 |
1 |
5 |
2 |
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| 3 |
(-1,3) |
c1 |
(1,0) |
e4 |
20 |
7 |
8 |
8 |
4 |
3 |
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| 4 |
(-1,3) |
c1 |
(1,-3) |
e7 |
20 |
9 |
7 |
3 |
5 |
3 |
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| 5 |
(-1,0) |
c4 |
(1,3) |
e1 |
21 |
2197 |
9 |
4 |
4 |
9 |
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| 6 |
(-1,0) |
c4 |
(-2,0) |
b4 |
21 (*) |
3266 |
8 |
3 |
4 |
6 |
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| 7 |
(-1,0) |
c4 |
(1,0) |
e4 |
21 (*) |
265 |
8 |
8 |
4 |
10 |
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| 8 |
(2,0) |
f4 |
(1,3) |
e1 |
20 |
667 |
9 |
4 |
4 |
14 |
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| 9 |
(2,0) |
f4 |
(-2,0) |
b4 |
20 (*) |
495 |
8 |
3 |
4 |
3 |
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| 10 |
(2,0) |
f4 |
(1,0) |
e4 |
20 (*) |
53 |
7 |
7 |
4 |
10 |
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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 Sweep |
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Eg. 12(8,UUR) indicates there exist 12 solutions
with different move sequences, |
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, Final Sweep) |
where the longest sweep is 8 and the final move
is the 3 sweep: UUR |
| (*) 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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| To match locations shown in standard
notation, reflection and/or reflection is generally needed. |
| Solution
differences can be very subtle. |
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