In Rubik's Cube FMC (Fewest Move Challenge), one of the popular methods is: EO (Edge Orientation) -> DR (Domino Reduction) -> HTR (Half Turn Reduction) -> Finish. This code computes the number of cases for their optimal number of moves in each steps. EO axis and DR axis are fixed. No NISS.
Average: 4.61 moves
| moves | num. | % | cum. | % |
|---|---|---|---|---|
| 0 | 1 | 0.05% | 1 | 0.05% |
| 1 | 2 | 0.10% | 3 | 0.15% |
| 2 | 25 | 1.22% | 28 | 1.37% |
| 3 | 202 | 9.86% | 230 | 11.23% |
| 4 | 620 | 30.27% | 850 | 41.50% |
| 5 | 900 | 43.95% | 1,750 | 85.45% |
| 6 | 285 | 13.92% | 2,035 | 99.37% |
| 7 | 13 | 0.63% | 2,048 | 100.00% |
Average: 7.80 moves
| moves | num. | % | cum. | % |
|---|---|---|---|---|
| 0 | 1 | 0.00% | 1 | 0.00% |
| 1 | 2 | 0.00% | 3 | 0.00% |
| 2 | 17 | 0.00% | 20 | 0.00% |
| 3 | 134 | 0.01% | 154 | 0.01% |
| 4 | 1,065 | 0.10% | 1,219 | 0.11% |
| 5 | 8,190 | 0.76%< 8000 /td> | 9,409 | 0.87% |
| 6 | 54,694 | 5.05% | 64,103 | 5.92% |
| 7 | 267,576 | 24.72% | 331,679 | 30.64% |
| 8 | 560,568 | 51.78% | 892,247 | 82.42% |
| 9 | 187,204 | 17.29% | 1,079,451 | 99.71% |
| 10 | 3,114 | 0.29% | 1,082,565 | 100.00% |
Average: 8.80 moves
| moves | num. | % | cum. | % |
|---|---|---|---|---|
| 0 | 1 | 0.00% | 1 | 0.00% |
| 1 | 2 | 0.01% | 3 | 0.01% |
| 2 | 9 | 0.03% | 12 | 0.04% |
| 3 | 36 | 0.12% | 48 | 0.16% |
| 4 | 124 | 0.42% | 172 | 0.59% |
| 5 | 530 | 1.80% | 702 | 2.39% |
| 6 | 1,806 | 6.14% | 2,508 | 8.53% |
| 7 | 3,732 | 12.69% | 6,240 | 21.22% |
| 8 | 5,158 | 17.54% | 11,398 | 38.77% |
| 9 | 7,070 | 24.05% | 18,468 | 62.82% |
| 10 | 7,218 | 24.55% | 25,686 | 87.37% |
| 11 | 3,202 | 10.89% | 28,888 | 98.26% |
| 12 | 488 | 1.66% | 29,376 | 99.92% |
| 13 | 24 | 0.08% | 29,400 | 100.00% |
Average: 10.13 moves
| moves | num. | % | cum. | % |
|---|---|---|---|---|
| 0 | 1 | 0.00% | 1 | 0.00% |
| 1 | 6 | 0.00% | 7 | 0.00% |
| 2 | 27 | 0.00% | 34 | 0.01% |
| 3 | 120 | 0.02% | 154 | 0.02% |
| 4 | 519 | 0.08% | 673 | 0.10% |
| 5 | 1,932 | 0.29% | 2,605 | 0.39% |
| 6 | 6,484 | 0.98% | 9,089 | 1.37% |
| 7 | 20,310 | 3.06% | 29,399 | 4.43% |
| 8 | 55,034 | 8.29% | 84,433 | 12.72% |
| 9 | 113,892 | 17.16% | 198,325 | 29.89% |
| 10 | 178,495 | 26.90% | 376,820 | 56.79% |
| 11 | 179,196 | 27.01% | 556,016 | 83.79% |
| 12 | 89,728 | 13.52% | 645,744 | 97.32% |
| 13 | 16,176 | 2.44% | 661,920 | 99.75% |
| 14 | 1,488 | 0.22% | 663,408 | 99.98% |
| 15 | 144 | 0.02% | 663,552 | 100.00% |
Average: 31.35 moves
| moves | num. | % | cum. | % |
|---|---|---|---|---|
| 0 | 1 | 0.00% | 1 | 0.00% |
| 1 | 12 | 0.00% | 13 | 0.00% |
| 2 | 126 | 0.00% | 139 | 0.00% |
| 3 | 1,244 | 0.00% | 1,383 | 0.00% |
| 4 | 10,748 | 0.00% | 12,131 | 0.00% |
| 5 | 85,468 | 0.00% | 97,599 | 0.00% |
| 6 | 650,349 | 0.00% | 747,948 | 0.00% |
| 7 | 4,730,159 | 0.00% | 5,478,107 | 0.00% |
| 8 | 32,275,893 | 0.00% | 37,754,000 | 0.00% |
| 9 | 207,004,813 | 0.00% | 244,758,813 | 0.00% |
| 10 | 1,243,629,538 | 0.00% | 1,488,388,351 | 0.00% |
| 11 | 6,915,341,475 | 0.00% | 8,403,729,826 | 0.00% |
| 12 | 35,602,806,961 | 0.00% | 44,006,536,787 | 0.00% |
| 13 | 171,480,473,587 | 0.00% | 215,487,010,374 | 0.00% |
| 14 | 779,541,895,273 | 0.00% | 995,028,905,647 | 0.00% |
| 15 | 3,357,154,264,295 | 0.00% | 4,352,183,169,942 | 0.00% |
| 16 | 13,707,343,918,919 | 0.00% | 18,059,527,088,861 | 0.00% |
| 17 | 53,045,954,984,718 | 0.00% | 71,105,482,073,579 | 0.00% |
| 18 | 194,461,816,648,957 | 0.00% | 265,567,298,722,536 | 0.00% |
| 19 | 675,354,135,568,276 | 0.00% | 940,921,434,290,812 | 0.00% |
| 20 | 2,223,116,895,537,360 | 0.01% | 3,164,038,329,828,170 | 0.01% |
| 21 | 6,933,320,406,823,760 | 0.02% | 10,097,358,736,651,900 | 0.02% |
| 22 | 20,435,787,843,490,800 | 0.05% | 30,533,146,580,142,700 | 0.07% |
| 23 | 56,642,419,955,303,200 | 0.13% | 87,175,566,535,445,900 | 0.20% |
| 24 | 146,489,449,992,806,000 | 0.34% | 233,665,016,528,252,000 | 0.54% |
| 25 | 349,840,166,413,364,000 | 0.81% | 583,505,182,941,616,000 | 1.35% |
| 26 | 762,435,696,540,331,000 | 1.76% | 1,345,940,879,481,950,000 | 3.11% |
| 27 | 1,499,050,028,765,180,000 | 3.47% | 2,844,990,908,247,130,000 | 6.58% |
| 28 | 2,632,709,795,461,090,000 | 6.09% | 5,477,700,703,708,220,000 | 12.66% |
| 29 | 4,097,124,756,498,850,000 | 9.47% | 9,574,825,460,207,070,000 | 22.14% |
| 30 | 5,611,340,947,886,110,000 | 12.97% | 15,186,166,408,093,200,000 | 35.11% |
| 31 | 6,711,570,449,396,530,000 | 15.52% | 21,897,736,857,489,700,000 | 50.63% |
| 32 | 6,927,517,651,309,780,000 | 16.02% | 28,825,254,508,799,500,000 | 66.64% |
| 33 | 6,050,078,686,278,600,000 | 13.99% | 34,875,333,195,078,100,000 | 80.63% |
| 34 | 4,345,112,170,139,990,000 | 10.05% | 39,220,445,365,218,100,000 | 90.68% |
| 35 | 2,480,810,785,772,970,000 | 5.74% | 41,701,256,150,991,000,000 | 96.41% |
| 36 | 1,089,112,502,010,310,000 | 2.52% | 42,790,368,653,001,400,000 | 98.93% |
| 37 | 357,740,563,194,137,000 | 0.83% | 43,148,109,216,195,500,000 | 99.76% |
| 38 | 86,402,930,810,907,500 | 0.20% | 43,234,512,147,006,400,000 | 99.96% |
| 39 | 15,282,998,739,947,500 | 0.04% | 43,249,795,145,746,300,000 | 99.99% |
| 40 | 1,998,835,931,328,460 | 0.00% | 43,251,793,981,677,700,000 | 100.00% |
| 41 | 194,890,805,882,880 | 0.00% | 43,251,988,872,483,500,000 | 100.00% |
| 42 | 13,751,073,068,352 | 0.00% | 43,252,002,623,556,600,000 | 100.00% |
| 43 | 635,024,960,064 | 0.00% | 43,252,003,258,581,600,000 | 100.00% |
| 44 | 15,768,311,040 | 0.00% | 43,252,003,274,349,900,000 | 100.00% |
| 45 | 139,905,792 | 0.00% | 43,252,003,274,489,800,000 | 100.00% |
Average: 5.94 moves
| moves | num. | % | cum. | % |
|---|---|---|---|---|
| 0 | 1 | 0.35% | 1 | 0.35% |
| 1 | 2 | 0.69% | 3 | 1.04% |
| 2 | 9 | 3.13% | 12 | 4.17% |
| 3 | 18 | 6.25% | 30 | 10.42% |
| 4 | 26 | 9.03% | 56 | 19.44% |
| 5 | 48 | 16.67% | 104 | 36.11% |
| 6 | 68 | 23.61% | 172 | 59.72% |
| 7 | 52 | 18.06% | 224 | 77.78% |
| 8 | 56 | 19.44% | 280 | 97.22% |
| 9 | 8 | 2.78% | 288 | 100.00% |
Average: 4.43 moves
| moves | num. | % | cum. | % |
|---|---|---|---|---|
| 0 | 1 | 0.52% | 1 | 0.52% |
| 1 | 4 | 2.08% | 5 | 2.60% |
| 2 | 10 | 5.21% | 15 | 7.81% |
| 3 | 24 | 12.50% | 39 | 20.31% |
| 4 | 53 | 27.60% | 92 | 47.92% |
| 5 | 64 | 33.33% | 156 | 81.25% |
| 6 | 31 | 16.15% | 187 | 97.40% |
| 7 | 4 | 2.08% | 191 | 99.48% |
| 8 | 1 | 0.52% | 192 | 100.00% |
Average: 8.64 moves
| moves | num. | % | cum. | % |
|---|---|---|---|---|
| 0 | 1 | 0.00% | 1 | 0.00% |
| 1 | 6 | 0.01% | 7 | 0.01% |
| 2 | 27 | 0.05% | 34 | 0.06% |
| 3 | 108 | 0.20% | 142 | 0.26% |
| 4 | 387 | 0.70% | 529 | 0.96% |
| 5 | 1,200 | 2.17% | 1,729 | 3.13% |
| 6 | 3,218 | 5.82% | 4,947 | 8.95% |
| 7 | 7,020 | 12.70% | 11,967 | 21.64% |
| 8 | 11,901 | 21.52% | 23,868 | 43.16% |
| 9 | 14,338 | 25.93% | 38,206 | 69.09% |
| 10 | 11,442 | 20.69% | 49,648 | 89.79% |
| 11 | 4,976 | 9.00% | 54,624 | 98.78% |
| 12 | 672 | 1.22% | 55,296 | 100.00% |