jumps, modern computers can easily examine all game positions in a reasonable time. The above sequence "PBP" has been entered as A112737 in OEIS. 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. It is also possible to generate all board positions. The results below have been obtained using the mcrl2 toolset (see the peg_solitaire example in the distribution). In the results below, it has generated all the board positions it really reached starting with the center vacant and finishing in the central hole. Solutions to the European game There are 3 initial non-congruent positions that have solutions. These are: 1) 0 1 2 3 4 5 6 0 o · · 1 · · · · · 2 · · · · · · · 3 · · · · · · · 4 · · · · · · · 5 · · · · · 6 · · · Possible solution: [2:2-0:2, 2:0-2:2, 1:4-1:2, 3:4-1:4, 3:2-3:4, 2:3-2:1, 5:3-3:3, 3:0-3:2, 5:1-3:1, 4:5-4:3, 5:5-5:3, 0:4-2:4, 2:1-4:1, 2:4-4:4, 5:2-5:4, 3:6-3:4, 1:1-1:3, 2:6-2:4, 0:3-2:3, 3:2-5:2, 3:4-3:2, 6:2-4:2, 3:2-5:2, 4:0-4:2, 4:3-4:1, 6:4-6:2, 6:2-4:2, 4:1-4:3, 4:3-4:5, 4:6-4:4, 5:4-3:4, 3:4-1:4, 1:5-1:3, 2:3-0:3, 0:2-0:4] 2) 0 1 2 3 4 5 6 0 · · · 1 · · o · · 2 · · · · · · · 3 · · · · · · · 4 · · · · · · · 5 · · · · · 6 · · · Possible solution: [1:1-1:3, 3:2-1:2, 3:4-3:2, 1:4-3:4, 5:3-3:3, 4:1-4:3, 2:1-4:1, 2:6-2:4, 4:4-4:2, 3:4-1:4, 3:2-3:4, 5:1-3:1, 4:6-2:6, 3:0-3:2, 4:5-2:5, 0:2-2:2, 2:6-2:4, 6:4-4:4, 3:4-5:4, 2:3-2:1, 2:0-2:2, 1:4-3:4, 5:5-5:3, 6:3-4:3, 4:3-4:1, 6:2-4:2, 3:2-5:2, 4:0-4:2, 5:2-3:2, 3:2-1:2, 1:2-1:4, 0:4-2:4, 3:4-1:4, 1:5-1:3, 0:3-2:3] and 3) 0 1 2 3 4 5 6 0 · · · 1 · · · · · 2 · · · o · · · 3 · · · · · · · 4 · · · · · · · 5 · · · · · 6 · · · Possible solution: [2:1-2:3, 0:2-2:2, 4:1-2:1, 4:3-4:1, 2:3-4:3, 1:4-1:2, 2:1-2:3, 0:4-0:2, 4:4-4:2, 3:4-1:4, 6:3-4:3, 1:1-1:3, 4:6-4:4, 5:1-3:1, 2:6-2:4, 1:4-1:2, 0:2-2:2, 3:6-3:4, 4:3-4:1, 6:2-4:2, 2:3-2:1, 4:1-4:3, 5:5-5:3, 2:0-2:2, 2:2-4:2, 3:4-5:4, 4:3-4:1, 3:0-3:2, 6:4-4:4, 4:0-4:2, 3:2-5:2, 5:2-5:4,