Peg Solitaire

29th January 2003: Solving this problem required the storage of 19,816,895,695 positions with 8 bytes per position (158,535,165,560 bytes=147 Gb).
28th January 2003: The final run on the french solitaire c1 lead to 280 unique solutions. Here are some remarkable solutions:







25th January 2003: After 3 months of computation, I just finished to compute the solutions of the french solitaire c1, and got a surprise, since it's possible in 20 moves (the previous records were 21 moves). I'm running the code to extract the solutions, so they will be available soon.
24th January 2003: Level 24 has 716,618,159 positions, level 25 has 341,762,350 positions, level 26 has 140,698,472 positions ! The levels above 26 are below.
23rd January 2003: Level 23 has 1,302,499,674 positions !
21st January 2003: Level 22 has 2,057,204,360 positions !
17th January 2003: Level 21 has 2,826,004,451 positions ! Level 22 will give around 2057559088 positions.
10th January 2003: Level 20 has 3,373,298,887 positions ! Level 21 will give around 2826251447 positions.
1st January 2003: Level 20 will give around 3373666315 positions.
30th December 2002: There are 3,489,271,180 positions at level 19 of the french solitaire c1 !
23rd December 2002: After a few weeks of computation, I have enumerated the number positions of the french solitaire c1 upto level 18. The number of positions is bigger than d2 and d3, since there is no symmetry on the c1 board. There will be around 3488773000 positions on level 19.

Level Number of positions
0 1
1 2
2 6
3 38
4 247
5 1567
6 9447
7 52619
8 266503
9 1222832
10 5045205
11 18529153
12 60017521
13 169761224
14 415258622
15 871660237
16 1562039335
17 2386129986
18 3114294699
19 3489271180
20 3373298887
21 2826004451
22 2057204360
23 1302499674
24 716618159
25 341762350
26 140698472
27 49626092
28 14851056
29 3725988
30 767077
31 125736
32 16010
33 1444
34 70
35 4
8th December 2002: I added a lot of new problems, and moved all solved problems to another page: PegSolitaireSolved.htm. A note about the new problems: they were taken from a Psion program from J Cade Roux, who took them from a 1924 book (The game Puzzle-Peg, Third Edition, 1924, Lubbers & Bell Mfg. Co., Clinton, Iowa, USA, 50 cents). I extracted the solutions and ran my solver on them, adding the solvable.
8th November 2002: The french d3 solitaire is now solved ! 21 moves are necessary. Total number of positions: 11,344,247,610
Level Number of positions
0 1
1 3
2 10
3 57
4 373
5 2258
6 12528
7 64105
8 298634
9 1257155
10 4745398
11 15894051
12 46858186
13 120691007
14 269904961
15 521971703
16 871301334
17 1255234462
18 1563562794
19 1689586369
20 1589238833
21 1304420373
22 935596167
23 586397031
24 320688468
25 152573663
26 62867136
27 22257151
28 6704181
29 1697465
30 354059
31 59168
32 7732
33 749
34 42
35 3
24th October 2002: All solutions of the english peg solitaire have been verified optimal with my program. Also, the french d2 solitaire is now complete. There are exactly 2376 solutions of 20 moves. I think half of these are symmetric. The full tree takes 94,188,275,408 bytes on my hard-disk (11,773,534,426 positions) ! Get the solutions here.
Level Number of positions
0 1
1 2
2 7
3 40
4 263
5 1617
6 9100
7 47935
8 229690
9 993055
10 3838722
11 13152057
12 39691485
13 104923514
14 241674174
15 482957038
16 834451235
17 1243706933
18 1598018491
19 1772709691
20 1702674373
21 1420029191
22 1030372529
23 650943881
24 357699207
25 170554788
26 70266254
27 24819507
28 7440972
29 1870379
30 385930
31 63406
32 8157
33 757
34 42
35 3
23rd September 2002: Added 19 problems, with some of their solutions (thanks to Alain Maye !). Matthew Daly reported a bug when using the Back function. Alain Maye solved the Lamp problem in 9 moves !
20th September 2002: Two persons asked me what notation is used for the moves. Well, this is quite simple. The board is stored into an array of 49 values, and each cell is numbered from 0 to 48 included. One move is stored as the number of the peg*4 + the direction of the peg (0=up, 1=right, 2=down, 3=left).
18th September 2002: Luigi Morelli is currently working on a new design of the pegs, which should be available soon.
11st September 2002: I don't include the solutions found by my program, since it's a game and I prefer that humans find the best solutions. Alain Maye sent a problem named "Arrow 3" with a solution in 10 moves (Alain Maye is the record holder of all french solitaires !).
If you want to cheat, I recommend that you use the program from Philippe Basciano called "Peg Solitaire 1.99". I use this program to compose new problems, since it is able to compute one solution, although non optimal !
9th September 2002: I finally finished to program the Javascript game. I rendered the marbles using this POV script. If you improve the rendering or if you want to include new problems, please mail to <euler@free.fr> !
1st September 2002: Finished the program to find the best number of moves. It requires a lot of memory to store solutions, and I don't want to spoil the fun by computing the solutions.
Pattern name Moves found Found by Best number of moves
L 3 ? 3
Latin Cross 5 ? 5
Small House     4
Small F     5
Half Fireplace     6
Small Pyramid     5
Plus     6
X     7
Crossbow     6
Fireplace     8
Small Diamond     5
Longbow     7
Star     8
Hat     8
Arrowhead     8
House     10
Short Lamp     6
Arrow 1     7
Pyramid     8
Arrow 2     8
Target     10
Bishop     8
Lamp     9
Symmetry     8
Highway     12
Hour-glass     11
Circle     9
Bar     12
Double Arrow     9
Symmetry 2     10
Big House     10
Tipi     10
Diamond     8
Pentagon     8
Spiral     10
Spiral 2     11
Four Forks     12
Lecturer     15
Truncated Triangle     10
Truncated Solitaire     13
New Square     13
Crossway     18
Four Knights     14
Svastika     17
Two Holes     18
Solitaire 14     18
Solitaire 18 Ernest Bergholt 18
Five Crosses     10
Crystal     11
Snow-flake     14
French Square     12
Octogon     13
Four Holes     ?

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