Number of Solutions of the No_Three_in_Line Problem on Small Grids n all . / - : x c o + * sum ------------------------------------------------------------------------------- 1 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 1 1 3 2 0 0 0 1 1 1 4 11 0 0 1 1 1 0 0 1 4 5 32 3 2 0 0 0 5 6 50 4 0 0 2 2 3 0 0 11 7 132 11 1 10 0 0 22 8 380 40 5 1 7 0 4 0 0 57 9 368 41 3 7 0 1 51 10 1135 132 3 0 13 1 6 0 1 156 11 1120 122 6 30 0 0 158 12 4348 524 3 0 33 2 4 0 0 566 13 3622 407 9 82 1 0 499 14 10568 1284 5 0 61 3 13 0 0 1366 15 30634 3681 13 283 1 0 3978 16 46304 5683 14 0 189 1 13 0 0 5900 17 .. 12 282 0 1 .. 18 .. 14 0 328 2 7 0 0 .. 19 .. 16 594 0 2 .. 20 .. 17 0 675 2 16 0 0 .. 21 .. 13 2413 0 1 .. 22 .. 18 0 1248 1 8 0 0 .. 23 .. 34 3968 1 1 .. 24 .. 43 0 2852 2 23 0 0 .. 25 .. 55 8983 2 3 .. 26 .. 1 0 36 0 0 .. 27 .. . 0 9 .. 28 .. 0 58 0 0 .. 29 .. 1 8 .. 30 .. 1 92 0 0 .. 31 .. 2 5 .. 32 .. 1 101 0 0 .. 33 .. . 0 14 .. 34 .. 0 172 0 0 .. 35 .. 1 23 .. 36 .. 1 281 0 0 .. 37 .. 0 21 .. 38 .. 1 337 0 0 .. 39 .. 0 33 .. 40 .. 0 541 0 0 .. 41 . 0 . . 42 .. 1 746 0 0 .. 43 . 0 . . 44 . 1 . 0 0 . 45 . 0 . . 46 . . 0 0 . 47 48 . . 0 0 . 49 50 . . 0 0 . 51 52 . . 0 . The column with heading * continues to be 0 for all n <= 82 . A number in the apropriate place gives the number of all existing solutions. . instead of a number means one known configuration. .. means some known configurations. ====================== last update: 31. Januar 1997 ====================== Heading abbreviations: ---------------------- n board size -- grid size all total number of solution . number of asymmetric solutions / number of solutions with exact one diagonal reflection symmetry - number of solutions with exact one orthogonal reflection symmetry : number of solutions with only half rotation symmetry x number of solutions with both diagonal reflection symmetries c number of solutions with quarter rotation symmetry except long diagonals o number of solutions with quarter rotation symmetry + number of solutions with both orthogonal reflection symmetries * number of solutions with all 8 symmetries of the grid sum number of solutions which are not equivalent under symmetry transformation