20:
1022:
i:i=ki,Jj,ik/lj,Ik,jl/AI,FD,CA,HJ,AI,JH/mk,Hl,Gm,fP,mk,Pf/ai,ca,fd,hj,ai,jh/gi,Mg,Lh,pd,gi,dp/Ki e:e=xe/lj,Ik,jl/ck,ac,df,lj,ck,jl/GI,lH,mG,DP,GI,PD/AI,FD,CA,JH,AI,HJ/pF,MK,gM,JL,MK,Fp/hj,ox,xe d:d=fd,xe,df/lj,ck,ac,Pf,ck,jl/DP,KI,PD/GI,lH,mG,DP,GI,PD/CK,DF,AC,LJ,CK,JL/MK,gM,hL,pF,MK,Fp/pd b:b=jb,lj/ck,ac,Pf,ck/DP,GI,mG,JH,GI,PD/LJ,CK,JL/MK,gM,hL,pF,MK,Fp/xo,dp,ox/xe/AI/BJ,JH,Hl,lj,jb b:x=jb,lj/ck,ac,Pf,ck/DP,GI,mG,JH,GI,PD/LJ,CK,JL/MK,gM,hL,pF,MK,Fp/xo,dp,ox/xe/AI/BJ,JH,Hl,lj,ex a:a=ca,jb,ac/lj,ck,jl/Ik,pP,KI,lj,Ik,jl/GI,lH,mG,DP,GI,PD/CK,DF,AC,LJ,CK,JL/dp,gi,pd,Mg,Lh,gi/ia a:p=ca,jb,ac/lj,ck,jl/Ik,pP,KI,lj,Ik,jl/GI,lH,mG,DP,GI,PD/CK,DF,AC,LJ,CK,JL/dp,gi,pd,Mg,Lh,gi/dp
542:
2222:
1026:
150:
105:
93:
158:
388:
positions and the number of covered C positions. Hence after an even number of moves all these three numbers are even, and after an odd number of moves all these three numbers are odd. Hence a final position with only one peg cannot be reached, since that would require that one of these numbers is one (the position of the peg, one is odd), while the other two numbers are zero, hence even.
387:
Initially with only the central position free, the number of covered A positions is 12, the number of covered B positions is 12, and also the number of covered C positions is 12. After every move the number of covered A positions increases or decreases by one, and the same for the number of covered B
1070:
umps). Interesting to note is that the shortest way to fail the game is in six moves, and the solution (besides its rotations and reflections) is unique. An example of this is as follows: 4 → 16; 23 → 9; 14 → 16; 17 → 15; 19 → 17; 31 → 23. (In this notation, the pegs are numbered from left to right,
525:
An unpublished study from 1989 on a generalized version of the game on the
English board showed that each possible problem in the generalized game has 2 possible distinct solutions, excluding symmetries, as the English board contains 9 distinct 3×3 sub-squares. One consequence of this analysis is to
373:
This mirror image notation is used, amongst other reasons, since on the
European board, one set of alternative games is to start with a hole at some position and to end with a single peg in its mirrored position. On the English board the equivalent alternative games are to start with a hole and end
1021:
x:x=ex,lj,ck,Pf,DP,GI,JH,mG,GI,ik,gi,LJ,JH,Hl,lj,jh,CK,pF,AC,CK,Mg,gi,ac,ck,kI,dp,pF,FD,DP,Pp,ox x:x=ex,lj,xe/hj,Ki,jh/ai,ca,fd,hj,ai,jh/MK,gM,hL,Fp,MK,pF/CK,DF,AC,JL,CK,LJ/PD,GI,mG,JH,GI,DP/Ox j:j=lj,Ik,jl/hj,Ki,jh/mk,Gm,Hl,fP,mk,Pf/ai,ca,fd,hj,ai,jh/MK,gM,hL,Fp,MK,pF/CK,DF,AC,JL,CK,LJ/Jj
2243:
A common triangular variant has five pegs on a side. A solution where the final peg arrives at the initial empty hole is not possible for a hole in one of the three central positions. An empty corner-hole setup can be solved in ten moves, and an empty midside-hole setup in nine (Bell 2008):
2217:
Peg solitaire has been played on other size boards, although the two given above are the most popular. It has also been played on a triangular board, with jumps allowed in all 3 directions. As long as the variant has the proper "parity" and is large enough, it will probably be solvable.
1510:. Note that the total number of reachable board positions (sum of the sequence) is 23,475,688, while the total number of possible board positions is 8,589,934,590 (33bit-1) (2^33), so only about 2.2% of all possible board positions can be reached starting with the center vacant.
526:
put a lower bound on the size of possible "inverted position" problems, in which the cells initially occupied are left empty and vice versa. Any solution to such a problem must contain a minimum of 11 moves, irrespective of the exact details of the problem.
781:
C-K p-F A-C-K M-g-i · · o · · o · · o · · o · o · · o · · o · · o · o · o o o o o o · o o o o o o · o o o o o
611:· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·
369:
English
European a b c a b c d e f y d e f z g h i j k l m g h i j k l m n o p x P O N n o p x P O N M L K J I H G M L K J I H G F E D Z F E D Y C B A C B A
54:
for one player involving movement of pegs on a board with holes. Some sets use marbles in a board with indentations. The game is known as solitaire in
Britain and as peg solitaire in the US where 'solitaire' is now the common name for
541:
518:
In 1999 peg solitaire was completely solved on a computer using an exhaustive search through all possible variants. It was achieved making use of the symmetries, efficient storage of board constellations and hashing.
1038:
The only place it is possible to end up with a solitary peg is the centre, or the middle of one of the edges; on the last jump, there will always be an option of choosing whether to end in the centre or the edge.
677:
m-G-I i-k g-i L-J-H-l-j-h · · o · · o · · o · · o · o · · o · · o · · o · · · · · o o
358:· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·
79:
The standard game fills the entire board with pegs except for the central hole. The objective is, making valid moves, to empty the entire board except for a solitary peg in the central hole.
505:
A solution for finding a pagoda function, which demonstrates the infeasibility of a given problem, is formulated as a linear programming problem and solvable in polynomial time.
377:
There is no solution to the
European board with the initial hole centrally located, if only orthogonal moves are permitted. This is easily seen as follows, by an argument from
2206:
0 1 2 3 4 5 6 0 · · · 1 · · · · · 2 · · · o · · · 3 · · · · · · · 4 · · · · · · · 5 · · · · · 6 · · ·
2197:
0 1 2 3 4 5 6 0 · · · 1 · · o · · 2 · · · · · · · 3 · · · · · · · 4 · · · · · · · 5 · · · · · 6 · · ·
2188:
0 1 2 3 4 5 6 0 o · · 1 · · · · · 2 · · · · · · · 3 · · · · · · · 4 · · · · · · · 5 · · · · · 6 · · ·
515:
A 1996 paper formulated a peg solitaire problem as a combinatorial optimization problem and discussed the properties of the feasible region called 'a solitaire cone'.
366:
There are many different solutions to the standard problem, and one notation used to describe them assigns letters to the holes (although numbers may also be used):
1029:
An easily remembered solution of first clearing edges by focusing on the holes circled in white – in figure 1, pegs are labelled in the order they are removed
394:
A tactic that can be used is to divide the board into packages of three and to purge (remove) them entirely using one extra peg, the catalyst, that
2927:
2550:
puzzle game, features many puzzles/games for the player to complete. The puzzle dubbed "Chinese
Checkers" is actually peg solitaire.
1507:
1075:
NOTE: If one board position can be rotated and/or flipped into another board position, the board positions are counted as identical.
462:
Other alternate games include starting with two empty holes and finishing with two pegs in those holes. Also starting with one hole
2777:
2602:
778:
o · · o · · o · · o · · o · · · · · · · · · · · ·
614:
P-f D-P G-I J-H · · o · · o · · o · · o · o
470:. On an English board, the hole can be anywhere and the final peg can only end up where multiples of three permit. Thus a hole at
459:
This technique can be used with a line of 3, a block of 2·3 and a 6-peg L shape with a base of length 3 and upright of length 4.
988:
2665:
508:
A paper in 1990 dealt with the generalized Hi-Q problems which are equivalent to the peg solitaire problems and showed their
19:
76:
contains a description of the board, rules and sample problems. This is the first known reference to the game in print.
2868:
2612:
2565:, the main antagonist, Vincent Volaju, spends most of his free time playing peg solitaire. The vector for his planned
3064:
2751:
2640:
Proc. 2nd Int. Conf. Computers and Games (CG 2000): Integer programming based algorithms for peg solitaire problems
984:
This solution was found in 1912 by Ernest
Bergholt and proven to be the shortest possible by John Beasley in 1964.
2547:
1499:
Since there can only be 31 jumps, modern computers can easily examine all game positions in a reasonable time.
549:
The shortest solution to the standard
English game involves 18 moves, counting multiple jumps as single moves:
3069:
391:
There are, however, several other configurations where a single initial hole can be reduced to a single peg.
70:, Princess of Soubise, with the puzzle by her side. The August 1697 edition of the French literary magazine
974:
a peg, you can solve the puzzle by following the solution in reverse, starting from the last picture, going
3059:
2556:
features the game at every table at their locations. The board featured is triangular with 15 total holes.
3054:
561:
e-x l-j c-k · · · · · · · · · · ·
2908:
1513:
It is also possible to generate all board positions. The results below have been obtained using the
2648:
2526:
On June 26, 1992, a video game based on peg solitaire was released for the Game Boy. Titled simply
66:, and the specific date of 1697, with an engraving made ten years later by Claude Auguste Berey of
2988:
2638:
Kiyomi, M.; Matsui, T. (2001), "Integer
Programming Based Algorithms for Peg Solitaire Problems",
3037:
2860:
2561:
2983:
2643:
502:
which is a strong tool to show the infeasibility of a given generalized peg solitaire problem.
2974:
Jefferson, Chris; et al. (October 2006), "Modelling and
Solving English Peg Solitairet",
2912:
533:
that there are only 5 fixed board positions where the game can successfully end with one peg.
2179:
1010:
Source peg and destination hole (the pegs jumped over are left as an exercise to the reader)
2896:
2543:
137:· · · · · · · · · · · · · · · · · · o · · · · · · · · · · · · · · · · · ·
67:
24:
2702:; Deza, A. (2001), "On the solitaire cone and its relationship to multi-commodity flows",
8:
3012:
2900:
1071:
starting with 0, and moving down each row and to the far left once each row is marked.)
674:· · o · · o · · · · · · · · · · · ·
3031:
2886:
2719:
2590:
169:
over an adjacent peg into a hole two positions away and then to remove the jumped peg.
132:· · · · · · · · · · · · · · · · o · · · · · · · · · · · · · · · ·
2864:
2661:
2618:
2608:
498:
A thorough analysis of the game is known. This analysis introduced a notion called
166:
2993:
2723:
2711:
2653:
963:
The order of some of the moves can be exchanged. Note that if you instead think of
530:
2221:
384:
A B C A B C A B A B C A B C A B C A B C A B C A B C A B C B C A B C A B C
117:
There are two traditional boards ('.' as an initial peg, 'o' as an initial hole):
509:
56:
2951:
2839:
2598:
2594:
2553:
72:
2997:
2530:, the game was developed by Hect. In North America, DTMC released the game as
522:
In 2001 an efficient method for solving peg solitaire problems was developed.
3048:
2657:
2622:
149:
2566:
1847:
reached starting with the center vacant and finishing in the central hole.
994:
Other solutions include the following list. In these, the notation used is
378:
1025:
381:. Divide the positions of the board into A, B and C positions as follows:
1058:
jumps, and the possibility of the same peg moved to make a further jump (
2891:
2715:
2699:
2642:, Lecture Notes in Computer Science, vol. 2063, pp. 229–240,
1033:
51:
2792:
63:
2808:
Implementation of brute force calculation of the Peg solitaire game
2231:(3) Asymmetrical 3-3-2-2 as described by George Bell, 20th century;
308:· · · · · · · · · · · · ·
104:
1843:
In the results below, it has generated all the board positions it
636:· · · · · · · · · · · · · · · · · · · · · · · · · · ·
626:
o · · · · · o o · · · · · o o · · · · · o o · · · · ·
62:
The first evidence of the game can be traced back to the court of
2680:
Uehara, R.; Iwata, S. (1990). "Generalized Hi-Q is NP-complete".
2570:
2378:
o o o o o
211:
Thus valid moves in each of the four orthogonal directions are:
2820:
Brassine, Michel (December 1981), "Découvrez... le solitaire",
977:
towards the first. However, this requires more than 18 moves.
157:
92:
1517:
toolset (see the peg_solitaire example in the distribution).
1514:
2738:
c't 07/1999 Spielverderber, Solitaire mit dem Computer lösen
1015:
a slash is used to separate 'chunks' such as a six-purge out
991:, which is designed to make memorizing the solution easier.
1503:
2938:
Cross, D. C. (1968), "Square solitaire and variations",
2877:
Bell, G. I. (2008), "Solving triangular peg solitaire",
555:
Shortest solution to English peg solitaire
2913:"A solitaire game and its relation to a finite field"
989:
a page that also introduces the Wolstenholme notation
545:
Interactive solution guide for English Peg Solitaire.
305:
On an English board, the first three moves might be:
3033:
Peg Solitaire: Easy to remember symmetrical solution
2250:
Shortest solution to triangular variant
2227:(1) French (European) style, 37 holes, 17th century;
1034:
Brute force attack on standard English peg solitaire
960:
o o o o o o o o o o o o
208:
is the hole of the peg that was jumped and removed.
2735:
2589:
620:· o · · o · · o · · · · ·
2173:
3046:
2316:· · · · · · · · · · · · · ·
536:
3017:Interactive Mathematics Miscellany and Puzzles
865:a-c-k-I d-p-F-D-P-p o-x
738:· · · · · · o · · · · · · o · · · · ·
192:is the hole the current peg moved from; a red
182:emboldened indicates the peg to be moved, and
2729:
1502:The above sequence "PBP" has been entered as
2637:
1054:ositions) of possible board positions after
948:o o o o o o o o o o · o
2679:
2229:(2) J. C. Wiegleb, 1779, Germany, 45 holes;
493:
2182:positions that have solutions. These are:
2987:
2890:
2647:
2285:· · · · · · ·
200:is the final position of that peg, a red
2819:
2698:
2633:
2631:
2604:Winning Ways for your Mathematical Plays
2220:
1024:
540:
156:
148:
18:
2785:
2278:· · ·
2233:(4) English style (standard), 33 holes;
3047:
2607:(2nd ed.), A K Peters/CRC Press,
2573:, is stored in peg solitaire marbles.
1042:Following is a table over the number (
758:· · · o · o o · · · o · o o ·
2740:(in German), vol. 7, p. 218
2673:
2628:
2583:
2537:
1850:
1520:
1079:
573:· · o · · o
161:Man playing triangular peg solitaire
2976:Computers & Operations Research
2940:Journal of Recreational Mathematics
2920:Journal of Recreational Mathematics
2857:The Ins & Outs of Peg Solitaire
2692:
13:
2848:
987:This solution can also be seen on
896:o o o o o o o o o o o o · o ·
850:· · o · ·
354:· · · · · · · · · · · · ·
316:· · o · ·
14:
3081:
3004:
2239:Grey = the hole for the survivor.
2212:
374:with a peg at the same position.
3030:White Pixels (24 October 2017),
3013:"Peg Solitaire and Group Theory"
2225:Peg solitaire game board shapes:
877:o o o o o o · o
186:indicates an empty hole. A blue
103:
91:
3040:from the original on 2021-12-11
2933:from the original on 2022-10-09
2828:
2736:Eichler; Jäger; Ludwig (1999),
474:can only leave a single peg at
452:→ o · ·
2813:
2769:
2744:
2174:Solutions to the European game
886:o o o o o o o · o
800:· · o o · · o · · o o
796:o o o o · · · · · o o · ·
348:· · · · · · o · · · · · ·
172:In the diagrams which follow,
165:A valid move is to jump a peg
1:
2576:
2521:
2263:= hole created by move;
537:Solutions to the English game
2879:Journal of Integer Sequences
2269:= jumped peg removed;
670:o · · · · ·
605:o · · · · o · · · · · ·
402:. In the example below, the
110:European peg solitaire board
7:
2840:George's Peg Solitaire Page
2782:volume #4 (second edition).
2752:"Mathematics and brainvita"
361:
322:· · · · · · · · · · ·
176:indicates a peg in a hole,
10:
3086:
2962:(6): 156–166, June 1962;
2297:· · · · · ·
2275:= hole filled by jumping;
846:· o o · o
2998:10.1016/j.cor.2005.01.018
2966:(2): 112–113, Feb. 1966;
2855:Beasley, John D. (1985),
2401:o o o o
2237:(6) Triangular, 15 holes.
16:Board game for one player
3065:Solitaire tabletop games
2954:, "Mathematical games",
2836:Generalized Cross Boards
2775:For Beasley's proof see
2704:Mathematical Programming
2658:10.1007/3-540-45579-5_15
579:· · · · · · · · · ·
494:Studies on peg solitaire
466:and ending with one peg
82:
2861:Oxford University Press
2562:Cowboy Bebop: The Movie
2259:= peg to move next;
1004:List of end target pegs
529:It can be proved using
144:
98:English solitaire board
27:playing solitaire, 1697
3011:Bogomolny, Alexander,
2240:
2235:(5) Diamond, 41 holes;
1030:
998:List of starting holes
546:
446:· → · →
162:
154:
28:
2224:
1028:
544:
160:
153:Playing Peg solitaire
152:
22:
3070:NP-complete problems
2756:Notes on Mathematics
2209:Possible solution:
2200:Possible solution:
2191:Possible solution:
2178:There are 3 initial
68:Anne de Rohan-Chabot
3060:Single-player games
2970:(5): 127, May 1966.
2956:Scientific American
2901:2007math......3865B
25:Princess of Soubise
3055:Mechanical puzzles
3036:(video), Youtube,
2885:: Article 08.4.8,
2716:10.1007/PL00011419
2569:attack, a type of
2546:, a horror-themed
2538:In popular culture
2241:
1031:
547:
406:is the catalyst.:
163:
155:
29:
2982:(10): 2935–2959,
2822:Jeux et Stratégie
2667:978-3-540-43080-3
2519:
2518:
2375:o · o · · o ·
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2007:
2006:
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2789:
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2766:
2765:
2763:
2758:, 28 August 2012
2748:
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2591:Berlekamp, E. R.
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840:· o
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828:o · o o o o
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818:o o o o · o
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585:· · · · · ·
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569:· ·
564:
552:
551:
531:abstract algebra
455:
451:
445:
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425:
420:
415:
400:jumps back again
357:
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342:· · · · o o
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44:Marble Solitaire
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2909:Bruijn, N.G. de
2907:
2892:math.CO/0703865
2876:
2871:
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2849:Further reading
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2579:
2548:point and click
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2500:o · o o o o
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2215:
2207:
2198:
2189:
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1841:
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1036:
1023:
961:
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539:
510:NP-completeness
500:pagoda function
496:
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85:
17:
12:
11:
5:
3083:
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3006:
3005:External links
3003:
3002:
3001:
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2874:
2870:978-0198532033
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2649:10.1.1.65.6244
2627:
2614:978-1568811307
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980:
979:
967:as a hole and
930:o o o o o · o
864:
780:
732:o · · · · · ·
710:o · o o o
676:
613:
599:· · · · ·
560:
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109:
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101:
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73:Mercure galant
15:
9:
6:
4:
3:
2:
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2989:10.1.1.5.7805
2985:
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2600:
2596:
2595:Conway, J. H.
2592:
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2258:
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2253:
2249:
2248:
2245:
2223:
2219:
2210:
2204:
2201:
2195:
2192:
2186:
2183:
2181:
2180:non-congruent
2166:
2158:
2155:
2154:
2150:
2147:
2146:
2142:
2139:
2138:
2134:
2131:
2130:
2126:
2123:
2122:
2118:
2115:
2114:
2110:
2107:
2106:
2102:
2099:
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1234:
1230:
1227:
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1216:
1213:
1212:
1209:
1202:
1199:
1196:
1195:
1191:
1188:
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1184:
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1177:
1174:
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1133:
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1125:
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1119:
1118:
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1111:
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1103:
1100:
1097:
1096:
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1027:
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1012:
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1006:
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1000:
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990:
985:
978:
975:
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966:
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934:
928:
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911:
906:
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857:
844:
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832:
822:
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804:
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789:
773:
765:
753:
748:
742:
736:
727:
719:
714:
708:
703:
694:
689:
668:
663:
651:
646:
640:
634:
624:
618:
609:
603:
594:
589:
583:
577:
568:
559:
558:
554:
553:
550:
543:
534:
532:
527:
523:
520:
516:
513:
511:
506:
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501:
491:
489:
485:
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477:
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469:
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436:
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411:
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389:
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375:
367:
352:
346:
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335:
326:
320:
311:
306:
299:
296:
292:
286:
278:
273:
269:
261:
256:
249:
244:
239:
233:
232:Jump to right
229:
224:
216:
212:
209:
205:
197:
180:
170:
168:
159:
151:
135:
130:
129:
125:
122:
121:
118:
106:
94:
80:
77:
75:
74:
69:
65:
60:
58:
53:
49:
45:
41:
37:
33:
32:Peg Solitaire
26:
21:
3032:
3020:, retrieved
3016:
2979:
2975:
2967:
2963:
2959:
2955:
2943:
2939:
2923:
2919:
2882:
2878:
2856:
2835:
2830:
2821:
2815:
2807:
2801:. Retrieved
2799:. 2020-08-31
2796:
2787:
2778:Winning Ways
2776:
2771:
2760:, retrieved
2755:
2746:
2737:
2731:
2710:(1): 27–57,
2707:
2703:
2694:
2685:
2682:Trans. IEICE
2681:
2675:
2639:
2603:
2585:
2567:Bioterrorism
2560:
2558:
2552:
2542:The PC game
2541:
2532:Lazlos' Leap
2531:
2527:
2525:
2510:
2501:
2490:
2487:
2482:
2476:
2470:
2465:
2459:
2454:
2437:
2431:
2426:
2420:
2415:
2409:
2403:
2392:
2389:
2385:
2380:
2371:
2362:
2357:
2352:
2348:
2343:
2335:
2332:
2327:
2323:
2318:
2312:
2307:
2298:
2290:
2286:
2279:
2271:
2265:
2256:
2255:
2242:
2216:
2208:
2202:
2199:
2193:
2190:
2184:
2177:
2164:
1844:
1842:
1834:
1512:
1501:
1498:
1490:
1074:
1073:
1067:
1063:
1059:
1055:
1051:
1047:
1043:
1041:
1037:
1014:
993:
986:
983:
976:
973:
968:
964:
962:
953:
944:
938:
936:o o o o
932:
926:
921:
909:
904:
902:o o o ·
898:
892:
890:o o o o
879:
870:
855:
842:
836:
830:
824:o o o o
820:
814:
808:
802:
792:
787:
771:
763:
751:
746:
740:
734:
725:
717:
712:
706:
701:
692:
687:
666:
661:
649:
644:
638:
632:
622:
616:
607:
601:
592:
587:
581:
575:
566:
548:
528:
524:
521:
517:
514:
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499:
497:
487:
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479:
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461:
458:
448:
439:
434:
428:
422:
417:
409:
403:
399:
395:
393:
390:
386:
379:Hans Zantema
376:
372:
365:
350:
344:
338:
333:
328:· · · ·
324:
318:
309:
304:
297:
294:
290:
284:
276:
271:
267:
259:
255:Jump to left
254:
247:
242:
237:
231:
227:
222:
214:
210:
203:
195:
178:
171:
167:orthogonally
164:
116:
78:
71:
61:
47:
43:
39:
35:
31:
30:
3022:7 September
2952:Gardner, M.
2926:: 133–137,
2824:(in French)
2762:6 September
2463:o o o
2338:· o · ·
2305:· ·
2301:· ·
1727:15,425,572
1719:22,106,348
1711:27,286,330
1703:28,994,876
1695:26,482,824
1673:20,773,236
1665:14,020,166
1007:Equals sign
3049:Categories
2803:2020-08-31
2793:"solboard"
2688:: 270–273.
2599:Guy, R. K.
2577:References
2522:Video game
2041:1,298,248
2033:1,639,652
2025:1,841,556
2003:1,841,556
1995:1,639,652
1987:1,298,248
1751:2,120,101
1743:4,792,664
1735:9,274,496
1657:8,171,208
1649:4,138,302
1641:1,834,379
916:o o o
744:o · · · o
52:board game
46:or simply
36:Solo Noble
2984:CiteSeerX
2946:: 121–123
2644:CiteSeerX
2623:316054929
2601:(2001) ,
2528:Solitaire
2493:o · o
2369:· o ·
2322:· ·
1355:1,160,977
1327:1,930,324
1316:2,765,623
1305:3,413,313
1294:3,626,632
1283:3,312,423
1272:2,598,215
1261:1,753,737
1250:1,022,224
412:· o
398:and then
396:jumps out
272:Jump down
126:European
64:Louis XIV
48:Solitaire
40:Solo Goli
3038:archived
2928:archived
2911:(1972),
2700:Avis, D.
2504:o o o o
2486:o o
2203:and 3)
2073:127,964
2065:285,740
2057:546,308
2049:902,056
1979:902,056
1971:546,308
1963:285,740
1955:127,964
1781:255,544
1773:800,152
1633:717,788
1625:249,690
1046:ossible
1013:, or / (
696:o o
362:Strategy
217:· o →
57:patience
2897:Bibcode
2724:7852133
2571:nanobot
2544:Shivers
2355:· o
2103:16,628
2081:49,236
1947:49,236
1925:16,628
1797:14,727
1789:68,236
1617:77,559
1595:21,842
1504:A112737
1388:100,565
1377:265,865
1366:600,372
1239:517,854
1228:229,614
1066:urther
432:·
295:Jump up
123:English
2986:
2867:
2797:github
2722:
2664:
2646:
2621:
2611:
2514:o o
2474:o o ·
2165:
2119:1,292
2111:5,012
1917:5,012
1909:1,292
1845:really
1835:
1805:2,529
1587:5,648
1579:1,338
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1413:1,715
1402:3,054
1399:32,250
1391:4,256
1380:4,356
1369:3,346
1358:1,972
1200:89,927
1189:31,312
862:o o o
656:· · ·
288:· →
282:o
274:o
265:· →
2931:(PDF)
2916:(PDF)
2887:arXiv
2720:S2CID
2095:Real
2017:Real
1939:Real
1861:Real
1515:mCRL2
1421:1,917
1410:8,688
1178:9,751
1167:2,757
1050:oard
1001:Colon
468:there
83:Board
50:is a
3024:2018
2865:ISBN
2838:in:
2834:See
2764:2018
2662:ISBN
2619:OCLC
2609:ISBN
2508:o o
2480:o o
2448:· ·
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2435:o o
2127:292
1901:292
1813:334
1765:PBP
1687:PBP
1609:PBP
1571:296
1531:PBP
1508:OEIS
1474:NFJ
1435:182
1424:665
1347:NFJ
1330:925
1319:373
1308:121
1220:NFJ
1093:NFJ
682:· ·
464:here
236:o ·
145:Play
23:The
2994:doi
2968:214
2964:214
2960:206
2712:doi
2654:doi
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2185:1)
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1893:60
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1471:PBP
1446:39
1432:348
1344:PBP
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1286:27
1264:10
1217:PBP
1156:719
1145:171
1090:PBP
971:as
486:or
240:→
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2992:,
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
