Table 1.

The number of positions in the game of checkers. For example, the possible positions for one piece include 32 squares for the Black king, 32 squares for the White king, 28 squares for a Black checker, and 28 squares for a White checker, for a total of 120 positions.

PiecesNumber of 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
Total 1-10 39,271,258,813,439
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 1-24 500,995,484,682,338,672,639