| 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 |
#(Longest Sweep, Final
Sweep) [Comment] |
| 1 |
(0,0) |
c3 |
(0,0) |
c3 |
15 (S) |
10 |
6 |
4 |
6 |
2 |
|
| 2 |
(3,0) |
c6 |
(0,0) |
c3 |
15 |
7 |
8 |
8 |
6 |
3 |
|
| 3 |
(3,3) |
f6 |
(0,0) |
c3 |
16 (S) |
1085 |
9 |
8 |
3 |
22 |
|
| 4 |
(3,0) |
c1 |
(3,0) |
c1 |
16 |
1732 |
10 |
10 |
3 |
61 |
|
| 5 |
(0,0) |
c4 |
(3,0) |
c1 |
15 |
62 |
8 |
7 |
4 |
6 |
|
| 6 |
(0,3) |
f4 |
(3,0) |
c1 |
15 |
62 |
8 |
7 |
5 |
6 |
|
| 7 |
(3,3) |
f1 |
(3,0) |
c1 |
16 |
1346 |
9 |
8 |
3 |
14 |
|
| 8 |
(3,3) |
a1 |
(3,3) |
a1 |
16 (S) |
215 |
9 |
9 |
5 |
17 |
|
| 9 |
(0,0) |
d4 |
(3,3) |
a1 |
15 (S) |
120 |
8 |
8 |
5 |
9 |
|
| 10 |
(3,0) |
d1 |
(3,3) |
a1 |
15 |
4 |
6 |
6 |
6 |
1 |
|
| 11 |
(0,2) |
c2 |
(0,2) |
c2 |
15 |
70 |
7 |
3 |
4 |
1 |
|
| 12 |
(3,2) |
f2 |
(0,2) |
c2 |
15 |
70 |
9 |
9 |
4 |
11 |
|
| 13 |
(0,-1) |
c5 |
(0,2) |
c2 |
15 |
110 |
8 |
7 |
4 |
5 |
|
| 14 |
(3,-1) |
f5 |
(0,2) |
c2 |
15 |
70 |
9 |
9 |
4 |
11 |
|
| 15 |
(3,2) |
a2 |
(3,2) |
a2 |
15 |
14 |
9 |
9 |
6 |
4 |
|
| 16 |
(0,2) |
d2 |
(3,2) |
a2 |
15 |
161 |
8 |
8 |
4 |
13 |
|
| 17 |
(0,-1) |
d5 |
(3,2) |
a2 |
15 |
200 |
8 |
8 |
4 |
15 |
|
| 18 |
(3,-1) |
a5 |
(3,2) |
a2 |
15 |
14 |
9 |
9 |
6 |
4 |
|
| 19 |
(2,2) |
b2 |
(2,2) |
b2 |
15 (S) |
136 |
6 |
6 |
4 |
4 |
|
| 20 |
(2,-1) |
e2 |
(2,2) |
b2 |
15 |
308 |
8 |
8 |
4 |
8 |
|
| 21 |
(-1,-1) |
e5 |
(2,2) |
b2 |
15 (S) |
172 |
8 |
8 |
4 |
12 |
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| 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 Sweep |
|
|
Eg. 12(8,UUR) indicates there exist 12 solutions
with different move sequences, |
|
|
, Final Sweep) |
where the longest sweep is 8 and the final move
is the 3 sweep: UUR |
| (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. |
|
| To match locations shown in standard
notation, reflection and/or reflection is generally needed. |
| Solution
differences can be very subtle. |
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