T O P S E C R E T Nim Operation Table ( X & Y = Target third pile ) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 -------------------------------------------------------------------------- 1: 0 3 2 5 4 7 6 9 8 11 10 13 12 15 14 17 16 19 18 2: 3 0 1 6 7 4 5 10 11 8 9 14 15 12 13 18 19 16 17 3: 2 1 0 7 6 5 4 11 10 9 8 15 14 13 12 19 18 17 16 4: 5 6 7 0 1 2 3 12 13 14 15 8 9 10 11 20 21 22 23 5: 4 7 6 1 0 3 2 13 12 15 14 9 8 11 10 21 20 23 22 6: 7 4 5 2 3 0 1 14 15 12 13 10 11 8 9 22 23 20 21 7: 6 5 4 3 2 1 0 15 14 13 12 11 10 9 8 23 22 21 20 8: 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 24 25 26 27 9: 8 11 10 13 12 15 14 1 0 3 2 5 4 7 6 25 24 27 26 10: 11 8 9 14 15 12 13 2 3 0 1 6 7 4 5 26 27 24 25 11: 10 9 8 15 14 13 12 3 2 1 0 7 6 5 4 27 26 25 24 12: 13 14 15 8 9 10 11 4 5 6 7 0 1 2 3 28 29 30 31 13: 12 15 14 9 8 11 10 5 4 7 6 1 0 3 2 29 28 31 30 14: 15 12 13 10 11 8 9 6 7 4 5 2 3 0 1 30 31 28 29 15: 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 31 30 29 28 16: 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 0 1 2 3 17: 16 19 18 21 20 23 22 25 24 27 26 29 28 31 30 1 0 3 2 18: 19 16 17 22 23 20 21 26 27 24 25 30 31 28 29 2 3 0 1 19: 18 17 16 23 22 21 20 27 26 25 24 31 30 29 28 3 2 1 0 20: 21 22 23 16 17 18 19 28 29 30 31 24 25 26 27 4 5 6 7 T O P S E C R E T Nim Operation Table ( X & Y = Target third pile ) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 -------------------------------------------------------------------------- 1: 0 3 2 5 4 7 6 9 8 11 10 13 12 15 14 17 16 19 18 2: 3 0 1 6 7 4 5 10 11 8 9 14 15 12 13 18 19 16 17 3: 2 1 0 7 6 5 4 11 10 9 8 15 14 13 12 19 18 17 16 4: 5 6 7 0 1 2 3 12 13 14 15 8 9 10 11 20 21 22 23 5: 4 7 6 1 0 3 2 13 12 15 14 9 8 11 10 21 20 23 22 6: 7 4 5 2 3 0 1 14 15 12 13 10 11 8 9 22 23 20 21 7: 6 5 4 3 2 1 0 15 14 13 12 11 10 9 8 23 22 21 20 8: 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 24 25 26 27 9: 8 11 10 13 12 15 14 1 0 3 2 5 4 7 6 25 24 27 26 10: 11 8 9 14 15 12 13 2 3 0 1 6 7 4 5 26 27 24 25 11: 10 9 8 15 14 13 12 3 2 1 0 7 6 5 4 27 26 25 24 12: 13 14 15 8 9 10 11 4 5 6 7 0 1 2 3 28 29 30 31 13: 12 15 14 9 8 11 10 5 4 7 6 1 0 3 2 29 28 31 30 14: 15 12 13 10 11 8 9 6 7 4 5 2 3 0 1 30 31 28 29 15: 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 31 30 29 28 16: 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 0 1 2 3 17: 16 19 18 21 20 23 22 25 24 27 26 29 28 31 30 1 0 3 2 18: 19 16 17 22 23 20 21 26 27 24 25 30 31 28 29 2 3 0 1 19: 18 17 16 23 22 21 20 27 26 25 24 31 30 29 28 3 2 1 0 20: 21 22 23 16 17 18 19 28 29 30 31 24 25 26 27 4 5 6 7