c1 d1 e1
c2 d2 e2
a3 b3 c3 d3 e3 f3 g3
a4 b4 c4 d4 e4 f4 g4
a5 b5 c5 d5 e5 f5 g5
c6 d6 e6
c7 d7 e7
B A B
C B C
B C C B C C B
A B B A B B A
B C C B C C B
C B C
B A B
Standard 7x7 Notation Hole Classification
(color coding used below).
(0,0) hole in bold.
English 33-Hole Board        
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, 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.
                       
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, regardless 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, Second Longest, Eg. 12(8,7,2) indicates there are 12 solutions with different move sequences, where
, 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
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 (can you spot the difference between the 2 Bergholt solutions?)

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