Killer Su Doku combinations by David Ireland www.di-mgt.com.au/sudoku.html First published 30 September 2005. Version 1.1 5 October 2005. Notation: N_k[t]=> there are t combinations of k distinct numbers 1-9 that add up to N. 3_2[1]={{2,1}} 4_2[1]={{3,1}} 5_2[2]={{4,1},{3,2}} 6_2[2]={{5,1},{4,2}} 6_3[1]={{3,2,1}} 7_2[3]={{6,1},{5,2},{4,3}} 7_3[1]={{4,2,1}} 8_2[3]={{7,1},{6,2},{5,3}} 8_3[2]={{5,2,1},{4,3,1}} 9_2[4]={{8,1},{7,2},{6,3},{5,4}} 9_3[3]={{6,2,1},{5,3,1},{4,3,2}} 10_2[4]={{9,1},{8,2},{7,3},{6,4}} 10_3[4]={{7,2,1},{6,3,1},{5,4,1},{5,3,2}} 10_4[1]={{4,3,2,1}} 11_2[4]={{9,2},{8,3},{7,4},{6,5}} 11_3[5]={{8,2,1},{7,3,1},{6,4,1},{6,3,2},{5,4,2}} 11_4[1]={{5,3,2,1}} 12_2[3]={{9,3},{8,4},{7,5}} 12_3[7]={{9,2,1},{8,3,1},{7,4,1},{7,3,2},{6,5,1},{6,4,2},{5,4,3}} 12_4[2]={{6,3,2,1},{5,4,2,1}} 13_2[3]={{9,4},{8,5},{7,6}} 13_3[7]={{9,3,1},{8,4,1},{8,3,2},{7,5,1},{7,4,2},{6,5,2},{6,4,3}} 13_4[3]={{7,3,2,1},{6,4,2,1},{5,4,3,1}} 14_2[2]={{9,5},{8,6}} 14_3[8]={{9,4,1},{9,3,2},{8,5,1},{8,4,2},{7,6,1},{7,5,2},{7,4,3},{6,5,3}} 14_4[5]={{8,3,2,1},{7,4,2,1},{6,5,2,1},{6,4,3,1},{5,4,3,2}} 15_2[2]={{9,6},{8,7}} 15_3[8]={{9,5,1},{9,4,2},{8,6,1},{8,5,2},{8,4,3},{7,6,2},{7,5,3},{6,5,4}} 15_4[6]={{9,3,2,1},{8,4,2,1},{7,5,2,1},{7,4,3,1},{6,5,3,1},{6,4,3,2}} 15_5[1]={{5,4,3,2,1}} 16_2[1]={{9,7}} 16_3[8]={{9,6,1},{9,5,2},{9,4,3},{8,7,1},{8,6,2},{8,5,3},{7,6,3},{7,5,4}} 16_4[8]={{9,4,2,1},{8,5,2,1},{8,4,3,1},{7,6,2,1},{7,5,3,1},{7,4,3,2},{6,5,4,1},{6,5,3,2}} 16_5[1]={{6,4,3,2,1}} 17_2[1]={{9,8}} 17_3[7]={{9,7,1},{9,6,2},{9,5,3},{8,7,2},{8,6,3},{8,5,4},{7,6,4}} 17_4[9]={{9,5,2,1},{9,4,3,1},{8,6,2,1},{8,5,3,1},{8,4,3,2},{7,6,3,1},{7,5,4,1},{7,5,3,2},{6,5,4,2}} 17_5[2]={{7,4,3,2,1},{6,5,3,2,1}} 18_3[7]={{9,8,1},{9,7,2},{9,6,3},{9,5,4},{8,7,3},{8,6,4},{7,6,5}} 18_4[11]={{9,6,2,1},{9,5,3,1},{9,4,3,2},{8,7,2,1},{8,6,3,1},{8,5,4,1},{8,5,3,2},{7,6,4,1},{7,6,3,2},{7,5,4,2},{6,5,4,3}} 18_5[3]={{8,4,3,2,1},{7,5,3,2,1},{6,5,4,2,1}} 19_3[5]={{9,8,2},{9,7,3},{9,6,4},{8,7,4},{8,6,5}} 19_4[11]={{9,7,2,1},{9,6,3,1},{9,5,4,1},{9,5,3,2},{8,7,3,1},{8,6,4,1},{8,6,3,2},{8,5,4,2},{7,6,5,1},{7,6,4,2},{7,5,4,3}} 19_5[5]={{9,4,3,2,1},{8,5,3,2,1},{7,6,3,2,1},{7,5,4,2,1},{6,5,4,3,1}} 20_3[4]={{9,8,3},{9,7,4},{9,6,5},{8,7,5}} 20_4[12]={{9,8,2,1},{9,7,3,1},{9,6,4,1},{9,6,3,2},{9,5,4,2},{8,7,4,1},{8,7,3,2},{8,6,5,1},{8,6,4,2},{8,5,4,3},{7,6,5,2},{7,6,4,3}} 20_5[6]={{9,5,3,2,1},{8,6,3,2,1},{8,5,4,2,1},{7,6,4,2,1},{7,5,4,3,1},{6,5,4,3,2}} 21_3[3]={{9,8,4},{9,7,5},{8,7,6}} 21_4[11]={{9,8,3,1},{9,7,4,1},{9,7,3,2},{9,6,5,1},{9,6,4,2},{9,5,4,3},{8,7,5,1},{8,7,4,2},{8,6,5,2},{8,6,4,3},{7,6,5,3}} 21_5[8]={{9,6,3,2,1},{9,5,4,2,1},{8,7,3,2,1},{8,6,4,2,1},{8,5,4,3,1},{7,6,5,2,1},{7,6,4,3,1},{7,5,4,3,2}} 21_6[1]={{6,5,4,3,2,1}} 22_3[2]={{9,8,5},{9,7,6}} 22_4[11]={{9,8,4,1},{9,8,3,2},{9,7,5,1},{9,7,4,2},{9,6,5,2},{9,6,4,3},{8,7,6,1},{8,7,5,2},{8,7,4,3},{8,6,5,3},{7,6,5,4}} 22_5[9]={{9,7,3,2,1},{9,6,4,2,1},{9,5,4,3,1},{8,7,4,2,1},{8,6,5,2,1},{8,6,4,3,1},{8,5,4,3,2},{7,6,5,3,1},{7,6,4,3,2}} 22_6[1]={{7,5,4,3,2,1}} 23_3[1]={{9,8,6}} 23_4[9]={{9,8,5,1},{9,8,4,2},{9,7,6,1},{9,7,5,2},{9,7,4,3},{9,6,5,3},{8,7,6,2},{8,7,5,3},{8,6,5,4}} 23_5[11]={{9,8,3,2,1},{9,7,4,2,1},{9,6,5,2,1},{9,6,4,3,1},{9,5,4,3,2},{8,7,5,2,1},{8,7,4,3,1},{8,6,5,3,1},{8,6,4,3,2},{7,6,5,4,1},{7,6,5,3,2}} 23_6[2]={{8,5,4,3,2,1},{7,6,4,3,2,1}} 24_3[1]={{9,8,7}} 24_4[8]={{9,8,6,1},{9,8,5,2},{9,8,4,3},{9,7,6,2},{9,7,5,3},{9,6,5,4},{8,7,6,3},{8,7,5,4}} 24_5[11]={{9,8,4,2,1},{9,7,5,2,1},{9,7,4,3,1},{9,6,5,3,1},{9,6,4,3,2},{8,7,6,2,1},{8,7,5,3,1},{8,7,4,3,2},{8,6,5,4,1},{8,6,5,3,2},{7,6,5,4,2}} 24_6[3]={{9,5,4,3,2,1},{8,6,4,3,2,1},{7,6,5,3,2,1}} 25_4[6]={{9,8,7,1},{9,8,6,2},{9,8,5,3},{9,7,6,3},{9,7,5,4},{8,7,6,4}} 25_5[12]={{9,8,5,2,1},{9,8,4,3,1},{9,7,6,2,1},{9,7,5,3,1},{9,7,4,3,2},{9,6,5,4,1},{9,6,5,3,2},{8,7,6,3,1},{8,7,5,4,1},{8,7,5,3,2},{8,6,5,4,2},{7,6,5,4,3}} 25_6[4]={{9,6,4,3,2,1},{8,7,4,3,2,1},{8,6,5,3,2,1},{7,6,5,4,2,1}} 26_4[5]={{9,8,7,2},{9,8,6,3},{9,8,5,4},{9,7,6,4},{8,7,6,5}} 26_5[11]={{9,8,6,2,1},{9,8,5,3,1},{9,8,4,3,2},{9,7,6,3,1},{9,7,5,4,1},{9,7,5,3,2},{9,6,5,4,2},{8,7,6,4,1},{8,7,6,3,2},{8,7,5,4,2},{8,6,5,4,3}} 26_6[5]={{9,7,4,3,2,1},{9,6,5,3,2,1},{8,7,5,3,2,1},{8,6,5,4,2,1},{7,6,5,4,3,1}} 27_4[3]={{9,8,7,3},{9,8,6,4},{9,7,6,5}} 27_5[11]={{9,8,7,2,1},{9,8,6,3,1},{9,8,5,4,1},{9,8,5,3,2},{9,7,6,4,1},{9,7,6,3,2},{9,7,5,4,2},{9,6,5,4,3},{8,7,6,5,1},{8,7,6,4,2},{8,7,5,4,3}} 27_6[7]={{9,8,4,3,2,1},{9,7,5,3,2,1},{9,6,5,4,2,1},{8,7,6,3,2,1},{8,7,5,4,2,1},{8,6,5,4,3,1},{7,6,5,4,3,2}} 28_4[2]={{9,8,7,4},{9,8,6,5}} 28_5[9]={{9,8,7,3,1},{9,8,6,4,1},{9,8,6,3,2},{9,8,5,4,2},{9,7,6,5,1},{9,7,6,4,2},{9,7,5,4,3},{8,7,6,5,2},{8,7,6,4,3}} 28_6[7]={{9,8,5,3,2,1},{9,7,6,3,2,1},{9,7,5,4,2,1},{9,6,5,4,3,1},{8,7,6,4,2,1},{8,7,5,4,3,1},{8,6,5,4,3,2}} 28_7[1]={{7,6,5,4,3,2,1}} 29_4[1]={{9,8,7,5}} 29_5[8]={{9,8,7,4,1},{9,8,7,3,2},{9,8,6,5,1},{9,8,6,4,2},{9,8,5,4,3},{9,7,6,5,2},{9,7,6,4,3},{8,7,6,5,3}} 29_6[8]={{9,8,6,3,2,1},{9,8,5,4,2,1},{9,7,6,4,2,1},{9,7,5,4,3,1},{9,6,5,4,3,2},{8,7,6,5,2,1},{8,7,6,4,3,1},{8,7,5,4,3,2}} 29_7[1]={{8,6,5,4,3,2,1}} 30_4[1]={{9,8,7,6}} 30_5[6]={{9,8,7,5,1},{9,8,7,4,2},{9,8,6,5,2},{9,8,6,4,3},{9,7,6,5,3},{8,7,6,5,4}} 30_6[8]={{9,8,7,3,2,1},{9,8,6,4,2,1},{9,8,5,4,3,1},{9,7,6,5,2,1},{9,7,6,4,3,1},{9,7,5,4,3,2},{8,7,6,5,3,1},{8,7,6,4,3,2}} 30_7[2]={{9,6,5,4,3,2,1},{8,7,5,4,3,2,1}} 31_5[5]={{9,8,7,6,1},{9,8,7,5,2},{9,8,7,4,3},{9,8,6,5,3},{9,7,6,5,4}} 31_6[8]={{9,8,7,4,2,1},{9,8,6,5,2,1},{9,8,6,4,3,1},{9,8,5,4,3,2},{9,7,6,5,3,1},{9,7,6,4,3,2},{8,7,6,5,4,1},{8,7,6,5,3,2}} 31_7[2]={{9,7,5,4,3,2,1},{8,7,6,4,3,2,1}} 32_5[3]={{9,8,7,6,2},{9,8,7,5,3},{9,8,6,5,4}} 32_6[7]={{9,8,7,5,2,1},{9,8,7,4,3,1},{9,8,6,5,3,1},{9,8,6,4,3,2},{9,7,6,5,4,1},{9,7,6,5,3,2},{8,7,6,5,4,2}} 32_7[3]={{9,8,5,4,3,2,1},{9,7,6,4,3,2,1},{8,7,6,5,3,2,1}} 33_5[2]={{9,8,7,6,3},{9,8,7,5,4}} 33_6[7]={{9,8,7,6,2,1},{9,8,7,5,3,1},{9,8,7,4,3,2},{9,8,6,5,4,1},{9,8,6,5,3,2},{9,7,6,5,4,2},{8,7,6,5,4,3}} 33_7[3]={{9,8,6,4,3,2,1},{9,7,6,5,3,2,1},{8,7,6,5,4,2,1}} 34_5[1]={{9,8,7,6,4}} 34_6[5]={{9,8,7,6,3,1},{9,8,7,5,4,1},{9,8,7,5,3,2},{9,8,6,5,4,2},{9,7,6,5,4,3}} 34_7[4]={{9,8,7,4,3,2,1},{9,8,6,5,3,2,1},{9,7,6,5,4,2,1},{8,7,6,5,4,3,1}} 35_5[1]={{9,8,7,6,5}} 35_6[4]={{9,8,7,6,4,1},{9,8,7,6,3,2},{9,8,7,5,4,2},{9,8,6,5,4,3}} 35_7[4]={{9,8,7,5,3,2,1},{9,8,6,5,4,2,1},{9,7,6,5,4,3,1},{8,7,6,5,4,3,2}} 36_6[3]={{9,8,7,6,5,1},{9,8,7,6,4,2},{9,8,7,5,4,3}} 36_7[4]={{9,8,7,6,3,2,1},{9,8,7,5,4,2,1},{9,8,6,5,4,3,1},{9,7,6,5,4,3,2}} 36_8[1]={{8,7,6,5,4,3,2,1}} 37_6[2]={{9,8,7,6,5,2},{9,8,7,6,4,3}} 37_7[3]={{9,8,7,6,4,2,1},{9,8,7,5,4,3,1},{9,8,6,5,4,3,2}} 37_8[1]={{9,7,6,5,4,3,2,1}} 38_6[1]={{9,8,7,6,5,3}} 38_7[3]={{9,8,7,6,5,2,1},{9,8,7,6,4,3,1},{9,8,7,5,4,3,2}} 38_8[1]={{9,8,6,5,4,3,2,1}} 39_6[1]={{9,8,7,6,5,4}} 39_7[2]={{9,8,7,6,5,3,1},{9,8,7,6,4,3,2}} 39_8[1]={{9,8,7,5,4,3,2,1}} 40_7[2]={{9,8,7,6,5,4,1},{9,8,7,6,5,3,2}} 40_8[1]={{9,8,7,6,4,3,2,1}} 41_7[1]={{9,8,7,6,5,4,2}} 41_8[1]={{9,8,7,6,5,3,2,1}} 42_7[1]={{9,8,7,6,5,4,3}} 42_8[1]={{9,8,7,6,5,4,2,1}} 43_8[1]={{9,8,7,6,5,4,3,1}} 44_8[1]={{9,8,7,6,5,4,3,2}} 45_9[1]={{9,8,7,6,5,4,3,2,1}}