Optimal ordering solutions
Individual solutions can be downloaded by clicking the corresponding link found in the Algorithm column or a zip containing all the solutions.
| n | k | Score | Algorithm |
|---|---|---|---|
| 2 | 1 | 1.33 | Optimum |
| 3 | 1 | 1.57 | Optimum |
| 3 | 2 | 1.75 | Optimum |
| 4 | 1 | 1.73 | Optimum |
| 4 | 2 | 2.55 | Optimum |
| 4 | 3 | 2.20 | Optimum |
| 5 | 1 | 1.84 | Optimum |
| 5 | 2 | 3.31 | Optimum |
| 5 | 3 | 4.19 | Optimum |
| 5 | 4 | 2.67 | Optimum |
| 6 | 1 | 1.90 | Optimum |
| 6 | 2 | 3.95 | Optimum |
| 6 | 3 | 6.40 | Optimum |
| 6 | 4 | 6.23 | Optimum |
| 6 | 5 | 3.14 | Optimum |
| 7 | 1 | 1.94 | GSE |
| 7 | 2 | 4.34 | GSE |
| 7 | 3 | 8.94 | GSE |
| 7 | 4 | 11.41 | GSE |
| 7 | 5 | 8.55 | GSE |
| 7 | 6 | 3.62 | GSE |
| 8 | 1 | 1.97 | GSE |
| 8 | 2 | 4.65 | GSE |
| 8 | 3 | 11.35 | GSE |
| 8 | 4 | 18.45 | GSE |
| 8 | 5 | 18.94 | GSE |
| 8 | 6 | 11.54 | GSE |
| 8 | 7 | 4.11 | GSE |
| 9 | 1 | 1.98 | GSE |
| 9 | 2 | 4.76 | GSE |
| 9 | 3 | 13.41 | GSE |
| 9 | 4 | 27.11 | GSE |
| 9 | 5 | 35.72 | GSE |
| 9 | 6 | 29.43 | GSE |
| 9 | 7 | 15.04 | GSE |
| 9 | 8 | 4.60 | GSE |
| 10 | 1 | 1.99 | GSE |
| 10 | 2 | 4.85 | GSE |
| 10 | 3 | 14.92 | GSE |
| 10 | 4 | 36.12 | GSE |
| 10 | 5 | 59.40 | GSE |
| 10 | 6 | 63.01 | GSE |
| 10 | 7 | 43.47 | GSE |
| 10 | 8 | 19.04 | GSE |
| 10 | 9 | 5.09 | GSE |
| 11 | 1 | 1.99 | GSE |
| 11 | 2 | 4.80 | GSE |
| 11 | 3 | 15.92 | GSE |
| 11 | 4 | 45.20 | GSE |
| 11 | 5 | 89.59 | GSE |
| 11 | 6 | 117.93 | GSE |
| 11 | 7 | 104.21 | GSE |
| 11 | 8 | 61.47 | GSE |
| 11 | 9 | 23.54 | GSE |
| 11 | 10 | 5.58 | GSE |
| 12 | 1 | 2.00 | GSE |
| 12 | 2 | 4.77 | GSE |
| 12 | 3 | 16.48 | GSE |
| 12 | 4 | 52.77 | GSE |
| 12 | 5 | 124.20 | GSE |
| 12 | 6 | 198.50 | GSE |
| 12 | 7 | 216.62 | GSE |
| 12 | 8 | 163.14 | GSE |
| 12 | 9 | 84.01 | GSE |
| 12 | 10 | 28.53 | GSE |
| 12 | 11 | 6.08 | GSE |
| 13 | 1 | 2.00 | GSE |
| 13 | 2 | 4.65 | GSE |
| 13 | 3 | 16.57 | GSE |
| 13 | 4 | 58.76 | GSE |
| 13 | 5 | 160.58 | GSE |
| 13 | 6 | 305.18 | GSE |
| 13 | 7 | 403.20 | GSE |
| 13 | 8 | 373.29 | GSE |
| 13 | 9 | 244.49 | GSE |
| 13 | 10 | 111.58 | GSE |
| 13 | 11 | 34.03 | GSE |
| 13 | 12 | 6.57 | GSE |
| 14 | 1 | 2.00 | GSE |
| 14 | 2 | 4.59 | GSE |
| 14 | 3 | 16.36 | GSE |
| 14 | 4 | 62.68 | GSE |
| 14 | 5 | 196.46 | GSE |
| 14 | 6 | 436.66 | GSE |
| 14 | 7 | 682.55 | GSE |
| 14 | 8 | 759.90 | GSE |
| 14 | 9 | 610.42 | GSE |
| 14 | 10 | 353.19 | GSE |
| 14 | 11 | 144.53 | GSE |
| 14 | 12 | 40.03 | GSE |
| 14 | 13 | 7.07 | GSE |
| 15 | 1 | 2.00 | GSE |
| 15 | 2 | 4.49 | GSE |
| 15 | 3 | 15.88 | GSE |
| 15 | 4 | 64.54 | GSE |
| 15 | 5 | 227.33 | GSE |
| 15 | 6 | 585.19 | GSE |
| 15 | 7 | 1069.52 | GSE |
| 15 | 8 | 1405.33 | GSE |
| 15 | 9 | 1349.38 | GSE |
| 15 | 10 | 954.46 | GSE |
| 15 | 11 | 494.64 | GSE |
| 15 | 12 | 183.55 | GSE |
| 15 | 13 | 46.53 | GSE |
| 15 | 14 | 7.56 | GSE |
| 16 | 1 | 2.00 | GSE |
| 16 | 2 | 4.44 | GSE |
| 16 | 3 | 15.45 | GSE |
| 16 | 4 | 64.59 | GSE |
| 16 | 5 | 252.52 | GSE |
| 16 | 6 | 741.38 | GSE |
| 16 | 7 | 1567.23 | GSE |
| 16 | 8 | 2394.47 | GSE |
| 16 | 9 | 2702.66 | GSE |
| 16 | 10 | 2277.75 | GSE |
| 16 | 11 | 1439.00 | GSE |
| 16 | 12 | 674.57 | GSE |
| 16 | 13 | 229.08 | GSE |
| 16 | 14 | 53.53 | GSE |
| 16 | 15 | 8.06 | GSE |
| 17 | 1 | 2.00 | GSE |
| 17 | 2 | 4.36 | GSE |
| 17 | 3 | 14.60 | GSE |
| 17 | 4 | 63.23 | GSE |
| 17 | 5 | 269.19 | GSE |
| 17 | 6 | 893.35 | GSE |
| 17 | 7 | 2160.85 | GSE |
| 17 | 8 | 3810.09 | GSE |
| 17 | 9 | 4980.14 | GSE |
| 17 | 10 | 4910.17 | GSE |
| 17 | 11 | 3684.96 | GSE |
| 17 | 12 | 2102.61 | GSE |
| 17 | 13 | 900.55 | GSE |
| 17 | 14 | 281.51 | GSE |
| 17 | 15 | 61.03 | GSE |
| 17 | 16 | 8.56 | GSE |
| 18 | 1 | 2.00 | GSE |
| 18 | 2 | 4.32 | GSE |
| 18 | 3 | 14.07 | GSE |
| 18 | 4 | 60.85 | GSE |
| 18 | 5 | 277.37 | GSE |
| 18 | 6 | 1028.54 | GSE |
| 18 | 7 | 2826.72 | GSE |
| 18 | 8 | 5694.18 | GSE |
| 18 | 9 | 8540.88 | GSE |
| 18 | 10 | 9720.97 | GSE |
| 18 | 11 | 8504.55 | GSE |
| 18 | 12 | 5748.63 | GSE |
| 18 | 13 | 2990.01 | GSE |
| 18 | 14 | 1178.43 | GSE |
| 18 | 15 | 341.53 | GSE |
| 18 | 16 | 69.02 | GSE |
| 18 | 17 | 9.05 | GSE |
| 19 | 1 | 2.00 | GSE |
| 19 | 2 | 4.26 | GSE |
| 19 | 3 | 13.38 | GSE |
| 19 | 4 | 57.56 | GSE |
| 19 | 5 | 277.82 | GSE |
| 19 | 6 | 1138.22 | GSE |
| 19 | 7 | 3522.35 | GSE |
| 19 | 8 | 8051.00 | GSE |
| 19 | 9 | 13746.43 | GSE |
| 19 | 10 | 17874.74 | GSE |
| 19 | 11 | 17982.38 | GSE |
| 19 | 12 | 14133.59 | GSE |
| 19 | 13 | 8692.41 | GSE |
| 19 | 14 | 4153.90 | GSE |
| 19 | 15 | 1516.35 | GSE |
| 19 | 16 | 409.51 | GSE |
| 19 | 17 | 77.52 | GSE |
| 19 | 18 | 9.55 | GSE |
| 20 | 1 | 2.00 | GSE |
| 20 | 2 | 4.23 | GSE |
| 20 | 3 | 12.80 | GSE |
| 20 | 4 | 54.23 | GSE |
| 20 | 5 | 271.64 | GSE |
| 20 | 6 | 1214.91 | GSE |
| 20 | 7 | 4385.89 | MIS |
| 20 | 8 | 11231.01 | MIS |
| 20 | 9 | 21546.31 | MIS |
| 20 | 10 | 31542.70 | MIS |
| 20 | 11 | 35959.83 | MIS |
| 20 | 12 | 32247.05 | MIS |
| 20 | 13 | 22905.12 | MIS |
| 20 | 14 | 12791.00 | GSE |
| 20 | 15 | 5654.22 | GSE |
| 20 | 16 | 1923.02 | GSE |
| 20 | 17 | 486.02 | GSE |
| 20 | 18 | 86.52 | GSE |
| 20 | 19 | 10.05 | GSE |
| 21 | 1 | 2.00 | MIS |
| 21 | 2 | 4.18 | GSE |
| 21 | 3 | 12.32 | GSE |
| 21 | 4 | 50.56 | GSE |
| 21 | 5 | 259.96 | GSE |
| 21 | 6 | 1319.08 | MIS |
| 21 | 7 | 5041.99 | MIS |
| 21 | 8 | 14469.44 | MIS |
| 21 | 9 | 31214.26 | MIS |
| 21 | 10 | 51517.82 | MIS |
| 21 | 11 | 66239.27 | MIS |
| 21 | 12 | 67376.56 | MIS |
| 21 | 13 | 54728.04 | MIS |
| 21 | 14 | 35605.07 | MIS |
| 21 | 15 | 18492.55 | MIS |
| 21 | 16 | 7581.02 | MIS |
| 21 | 17 | 2405.56 | MIS |
| 21 | 18 | 571.59 | MIS |
| 21 | 19 | 96.02 | MIS |
| 21 | 20 | 10.55 | MIS |
| 22 | 1 | 2.00 | MIS |
| 22 | 2 | 4.17 | GSE |
| 22 | 3 | 11.88 | GSE |
| 22 | 4 | 47.23 | GSE |
| 22 | 5 | 244.72 | GSE |
| 22 | 6 | 1327.66 | MIS |
| 22 | 7 | 5583.60 | MIS |
| 22 | 8 | 17858.30 | MIS |
| 22 | 9 | 43138.55 | MIS |
| 22 | 14 | 89781.46 | MIS |
| 22 | 15 | 53875.71 | MIS |
| 22 | 16 | 25998.94 | MIS |
| 22 | 17 | 9969.62 | MIS |
| 22 | 18 | 2973.20 | MIS |
| 22 | 19 | 666.60 | MIS |
| 22 | 20 | 106.02 | MIS |
| 22 | 21 | 11.04 | MIS |
| 23 | 1 | 2.00 | MIS |
| 23 | 2 | 4.13 | GSE |
| 23 | 3 | 11.49 | GSE |
| 23 | 4 | 44.00 | GSE |
| 23 | 5 | 227.36 | GSE |
| 23 | 6 | 1302.41 | MIS |
| 23 | 7 | 5982.36 | MIS |
| 23 | 8 | 21198.29 | MIS |
| 23 | 16 | 79622.89 | MIS |
| 23 | 17 | 35897.21 | MIS |
| 23 | 18 | 12923.35 | MIS |
| 23 | 19 | 3635.29 | MIS |
| 23 | 20 | 771.62 | MIS |
| 23 | 21 | 116.52 | MIS |
| 23 | 22 | 11.54 | MIS |
| 24 | 1 | 2.00 | MIS |
| 24 | 2 | 4.12 | GSE |
| 24 | 3 | 11.16 | GSE |
| 24 | 4 | 41.13 | GSE |
| 24 | 5 | 209.28 | GSE |
| 24 | 6 | 1249.69 | MIS |
| 24 | 7 | 6214.05 | MIS |
| 24 | 17 | 115192.75 | MIS |
| 24 | 18 | 48735.39 | MIS |
| 24 | 19 | 16540.86 | MIS |
| 24 | 20 | 4402.60 | MIS |
| 24 | 21 | 887.12 | MIS |
| 24 | 22 | 127.52 | MIS |
| 24 | 23 | 12.04 | MIS |
| 25 | 1 | 2.00 | MIS |
| 25 | 2 | 4.10 | GSE |
| 25 | 3 | 10.83 | GSE |
| 25 | 4 | 38.53 | GSE |
| 25 | 5 | 191.27 | GSE |
| 25 | 6 | 1176.10 | MIS |
| 25 | 7 | 6281.03 | MIS |
| 25 | 18 | 163556.91 | MIS |
| 25 | 19 | 65175.35 | MIS |
| 25 | 20 | 20920.20 | MIS |
| 25 | 21 | 5285.11 | MIS |
| 25 | 22 | 1013.58 | MIS |
| 25 | 23 | 139.02 | MIS |
| 25 | 24 | 12.54 | MIS |
| 26 | 1 | 2.00 | MIS |
| 26 | 2 | 4.09 | GSE |
| 26 | 3 | 10.57 | GSE |
| 26 | 4 | 36.27 | GSE |
| 26 | 5 | 174.32 | GSE |
| 26 | 6 | 1089.00 | MIS |
| 26 | 7 | 6190.99 | MIS |
| 26 | 20 | 85976.81 | MIS |
| 26 | 21 | 26178.85 | MIS |
| 26 | 22 | 6293.77 | MIS |
| 26 | 23 | 1151.61 | MIS |
| 26 | 24 | 151.02 | MIS |
| 26 | 25 | 13.04 | MIS |
| 27 | 1 | 2.00 | MIS |
| 27 | 2 | 4.07 | GSE |
| 27 | 3 | 10.35 | GSE |
| 27 | 4 | 34.32 | GSE |
| 27 | 5 | 158.70 | GSE |
| 27 | 6 | 995.25 | MIS |
| 27 | 21 | 112030.98 | MIS |
| 27 | 22 | 32447.29 | MIS |
| 27 | 23 | 7440.29 | MIS |
| 27 | 24 | 1301.63 | MIS |
| 27 | 25 | 163.52 | MIS |
| 27 | 26 | 13.54 | MIS |
| 28 | 1 | 2.00 | MIS |
| 28 | 2 | 4.07 | GSE |
| 28 | 3 | 10.17 | GSE |
| 28 | 4 | 32.60 | GSE |
| 28 | 5 | 149.76 | MIS |
| 28 | 6 | 899.75 | MIS |
| 28 | 22 | 144339.74 | MIS |
| 28 | 23 | 39857.85 | MIS |
| 28 | 24 | 8737.03 | MIS |
| 28 | 25 | 1464.10 | MIS |
| 28 | 26 | 176.52 | MIS |
| 28 | 27 | 14.03 | MIS |
| 29 | 1 | 2.00 | MIS |
| 29 | 2 | 4.05 | GSE |
| 29 | 3 | 10.01 | GSE |
| 29 | 4 | 31.11 | GSE |
| 29 | 5 | 136.38 | MIS |
| 29 | 6 | 806.88 | MIS |
| 29 | 23 | 184045.06 | MIS |
| 29 | 24 | 48566.24 | MIS |
| 29 | 25 | 10195.60 | MIS |
| 29 | 26 | 1639.64 | MIS |
| 29 | 27 | 190.02 | MIS |
| 29 | 28 | 14.53 | MIS |
| 30 | 1 | 2.00 | MIS |
| 30 | 2 | 4.05 | GSE |
| 30 | 3 | 9.85 | GSE |
| 30 | 4 | 29.82 | GSE |
| 30 | 5 | 124.63 | MIS |
| 30 | 6 | 719.71 | MIS |
| 30 | 25 | 58729.42 | MIS |
| 30 | 26 | 11829.74 | MIS |
| 30 | 27 | 1828.63 | MIS |
| 30 | 28 | 204.02 | MIS |
| 30 | 29 | 15.03 | MIS |
| 31 | 1 | 2.00 | MIS |
| 31 | 2 | 4.04 | GSE |
| 31 | 3 | 9.72 | GSE |
| 31 | 4 | 29.02 | MIS |
| 31 | 5 | 114.54 | MIS |
| 31 | 26 | 70523.20 | MIS |
| 31 | 27 | 13652.67 | MIS |
| 31 | 28 | 2031.61 | MIS |
| 31 | 29 | 218.52 | MIS |
| 31 | 30 | 15.53 | MIS |
| 32 | 1 | 2.00 | MIS |
| 32 | 2 | 4.04 | GSE |
| 32 | 3 | 9.60 | GSE |
| 32 | 4 | 28.06 | MIS |
| 32 | 5 | 105.91 | MIS |
| 32 | 27 | 84142.65 | MIS |
| 32 | 28 | 15674.21 | MIS |
| 32 | 29 | 2249.13 | MIS |
| 32 | 30 | 233.51 | MIS |
| 32 | 31 | 16.03 | MIS |