Relative Effort Generating the No_Three_in_Line Solutions on Small Grids n . / - : x c o + * --------------------------------------------------------------------- 1 - - - - - 2 3.00 2.00 - 1.00 1.00 - - - 3 2.67 2.50 2.00 1.00 1.00 4 4.00 1.80 5.00 3.00 4.00 2.00 2.00 2.00 5 3.91 2.33 1.00 1.00 3.00 6 4.38 2.24 4.20 4.33 1.75 3.00 2.00 1.50 7 4.48 1.75 1.77 1.14 2.33 8 5.65 2.78 3.33 3.26 2.50 5.17 2.25 1.33 9 6.17 2.13 1.38 1.10 3.43 10 6.72 2.94 6.51 5.03 2.14 1.61 1.56 1.25 11 7.43 2.16 1.48 1.28 1.42 12 7.73 3.26 4.75 5.27 2.32 2.68 2.00 1.60 13 7.24 2.24 1.83 1.28 4.44 14 9.15 3.14 7.25 5.33 2.16 3.19 2.14 1.38 15 11.65 2.57 2.17 1.22 2.44 16 7.79 3.39 7.89 4.53 2.28 2.85 2.17 1.82 17 2.53 1.58 1.22 2.84 18 3.55 7.96 6.42 2.34 3.02 2.12 1.65 19 2.56 2.00 1.31 3.40 20 3.91 8.25 6.20 2.40 3.47 2.57 1.52 21 2.83 2.03 1.25 3.25 22 3.62 9.81 5.67 2.34 3.43 2.33 1.56 23 2.90 2.64 1.34 3.43 24 9.22 5.20 2.41 3.94 2.57 1.54 25 2.09 1.33 3.72 26 11.43 2.41 3.69 2.67 1.58 27 1.34 3.59 28 2.50 3.82 2.67 1.53 29 1.37 3.82 30 2.49 4.14 2.65 1.61 31 1.34 3.84 32 2.55 4.08 2.68 1.51 33 1.93 4.18 34 2.54 4.10 2.86 1.65 35 1.45 4.22 36 2.54 4.26 3.44 1.66 37 1.37 4.03 38 2.61 4.07 2.77 1.66 39 1.44 40 2.53 4.65 3.08 1.61 41 1.45 42 4.46 2.95 1.67 43 44 2.66 3.06 1.67 45 1.47 46 3.47 1.70 47 48 3.25 1.70 49 50 3.46 1.77 51 52 1.74 53 54 1.73 55 56 1.79 57 58 1.73 The column with heading * continues to be < 2.00 for all n <= 82 . ====================== last update: 1. Januar 1997 ====================== Heading abbreviations: ---------------------- n board size -- grid size . 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