include("/usr/brazeau/misc/chinook/web_docs/php/header.php"); include("/usr/brazeau/misc/chinook/web_docs/php/breadcrumb.php"); printHeader("Total Number of Checker Positions"); printBreadCrumbTrail("Total Number of Checker Positions"); ?>
Here are the total number of checker positions sorted according to the number of pieces on the board.
# PIECES # POSITIONS 1 120 2 6,972 3 261,224 4 7,092,774 5 148,688,232 6 2,503,611,964 7 34,779,531,480 8 406,309,208,481 9 4,048,627,642,976 10 34,778,882,769,216 11 259,669,578,902,016 12 1,695,618,078,654,976 13 9,726,900,031,328,256 14 49,134,911,067,979,776 15 218,511,510,918,189,056 16 852,888,183,557,922,816 17 2,905,162,728,973,680,640 18 8,568,043,414,939,516,928 19 21,661,954,506,100,113,408 20 46,352,957,062,510,379,008 21 82,459,728,874,435,248,128 22 118,435,747,136,817,856,512 23 129,406,908,049,181,900,800 24 90,072,726,844,888,186,880 Total: 500,995,484,682,338,672,639
Of particular interest are those positions where either the material is even if there is an even number of pieces on the board, or the difference is no more than one when there are an odd number of pieces present (for example, 4 vs 3 and 3 vs 4 for 7 pieces).
1 vs 0: 60 (x 2) 1 vs 1: 3,488 2 vs 1: 98,016 (x 2) 2 vs 2: 2,662,932 3 vs 2: 46,520,744 (x 2) 3 vs 3: 783,806,128 4 vs 3: 9,527,629,380 (x 2) 4 vs 4: 111,378,534,401 5 vs 4: 998,874,699,888 (x 2) 5 vs 5: 8,586,481,972,128 6 vs 5: 58,769,595,279,296 (x 2) 6 vs 6: 384,033,878,250,176 7 vs 6: 2,046,244,120,757,760 (x 2) 7 vs 7: 10,359,927,057,187,840 8 vs 7: 43,428,742,062,013,440 (x 2) 8 vs 8: 171,975,762,422,069,760 9 vs 8: 569,058,493,921,640,448 (x 2) 9 vs 9: 1,765,698,358,650,175,488 A vs 9: 4,596,454,069,579,874,304 (x 2) A vs A: 11,113,460,838,901,284,864 B vs A: 22,520,313,165,772,750,848 (x 2) B vs B: 41,842,926,176,229,654,528 C vs B: 64,703,454,024,590,950,400 (x 2) C vs C: 90,072,726,844,888,186,880 Total number of positions: 329,847,169,676,858,217,781include("/usr/brazeau/misc/chinook/web_docs/php/trailer.php"); ?>