| English 33-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, Second longest,
Final) [Comment] |
| 1 |
(0,0) |
d4 |
(0,0) |
d4 |
18 |
2 (S) |
5 |
1 |
5 |
1 |
1(5,5,1), 1(5,4,1) [Bergholt solution(s)] |
| 2 |
(3,0) |
d1 |
(0,0) |
d4 |
18 |
2 (S) |
5 |
1 |
5 |
1 |
2(5,U) [Equivalent to previous problem] |
| 3 |
(3,0) |
d1 |
(3,0) |
d1 |
18 |
3 (S) |
5 |
5 |
5 |
1 |
3(5,RURDR) |
| 4 |
(-3,0) |
d1 |
(3,0) |
d7 |
18 |
27 (S) |
6 |
6 |
5 |
3 |
18(6,LDDRUR), 1(5,RURDR), 8(5,DDRUR) |
| 5 |
(0,3) |
d1 |
(3,0) |
a4 |
17 |
2 |
6 |
6 |
6 |
1 |
2(6,DLDRUR) [Bergholt #1 modified] |
| 6 |
(0,0) |
d4 |
(3,0) |
d1 |
17 |
2 (S) |
6 |
6 |
6 |
1 |
2(6,DLDRUR) [Bergholt #1 modified] |
| 7 |
(1,0) |
d3 |
(1,0) |
d3 |
16 |
6 (S) |
7 |
7 |
5 |
2 |
4(7,LULDDRU), 2(5,LLDRU) |
| 8 |
(1,3) |
c1 |
(1,0) |
c4 |
16 |
6 |
7 |
7 |
5 |
2 |
4(7,LULDDRU), 2(5,LLDRU) [Same result as previous] |
| 9 |
(-2,0) |
d2 |
(1,0) |
d5 |
17 |
2 (S) |
5 |
4 |
5 |
1 |
2(5,RDRU) |
| 10 |
(2,0) |
d2 |
(2,0) |
d2 |
19 |
62 (S) |
7 |
2 |
4 |
2 |
3(7,R), 5(6,UR), 14(5,UR), 3(5,R), 16(4,UR), 21(4,R) |
| 11 |
(-1,0) |
d3 |
(2,0) |
d6 |
17 |
2 (S) |
5 |
1 |
5 |
1 |
2(5,R) |
| 12 |
(-1,3) |
c1 |
(2,0) |
f4 |
17 |
2 |
5 |
1 |
5 |
1 |
2(5,R) [Same result as previous] |
| 13 |
(3,1) |
c1 |
(3,1) |
c1 |
16 |
1835 |
8 |
7 |
4 |
30 |
3(8,RRDRU),
10(8,LDRU), 3(8,RRUR), 2(8,UUR), 6(8,DR), 8(7,RDLDRRU), etc. |
| 14 |
(0,1) |
d3 |
(3,1) |
a3 |
16 |
3056 |
8 |
6 |
4 |
21 |
3(8,UUR), 13(8,DR), 1(7,UURDRU),
1(7,DRDRU), 2(7,DDRUR), 6(7,URUR), etc. |
| 15 |
(-3,1) |
c1 |
(3,1) |
c7 |
16 |
1750 |
8 |
6 |
4 |
22 |
1(8,UUR), 7(8,DR),
1(7,UURDRU), 2(7,DRRUR), 1(7,DRDRU), 1(7,DDRUR), etc. |
| 16 |
(0,-2) |
d2 |
(3,1) |
a5 |
17 |
460 |
7 |
7 |
4 |
17 |
2(7,DRURDRU),
3(7,URUR), 3(7,DR), 1(6,RDRURU), 4(6,UURDRU), 1(6,LDRU), etc. |
| 17 |
(1,1) |
c3 |
(1,1) |
c3 |
15 |
14 (S) |
5 |
4 |
5 |
5 |
2(5,RURD), 2(5,LUUR), 2(5,URUL), 4(5,DLU), 4(5,UL) |
| 18 |
(-2,1) |
c2 |
(1,1) |
c5 |
15 |
8 |
5 |
3 |
5 |
2 |
4(5,DLU), 4(5,UL) |
| 19 |
(2,1) |
c2 |
(2,1) |
c2 |
16 |
2529 |
8 |
7 |
4 |
14 |
4(8,RR), 4(8,DR),
19(7,UULDRRU), 4(7,UUR), 4(7,LUR), 4(7,RR), 26(7,DR), etc. |
| 20 |
(-1,1) |
c3 |
(2,1) |
f3 |
16 |
5079 |
8 |
7 |
4 |
23 |
8(8,RR), 18(8,DR),
96(7,UULDRRU), 2(7,DLDRUR), 4(7,ULURR), 4(7,DRUR), etc. |
| 21 |
(-1,-2) |
c2 |
(2,1) |
f5 |
16 |
139 |
7 |
6 |
4 |
10 |
2(7,DRUR),
2(7,URR), 20(6,DLDRRU), 10(6,URR), 33(5,ULURR), 8(5,LDRU), etc. |
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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,
regardless 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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| To match locations shown in standard
notation, reflection and/or reflection is generally needed. |
| Solution
differences can be very subtle (can you spot the difference between the 2
Bergholt solutions?) |
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