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cubezone cross study lars vandenbergh s cubezone speedcubing taken one step further algorithms zb f2l oll pll coll methods square 1 tools imagecube imagerevenge articles cross study cross study this short article describes the results of a computer analysis i did for solving the cross of the first layer in the least number of moves in this study we are trying to determine the required number of moves to the solve the cross for all possible cases if we would always be able to see an optimal solution god s algorithm from that information we can then calculate the average and maximum number of moves that a perfect cross solver would need to solve the cross from a random state most cross first speedcubers always start with the same color when building the cross a lot of people can still comfortably build the cross on the opposite face of their prefered color and a few people are completely color neutral and start building the cross on whichever face it seems the easiest in this computer study we have investigated all three scenarios fixed color cross solving when solving the cross on the same face there are 4 edge pieces that we need to take into account they can each be oriented in 2 ways and can placed in 12 locations the amount of cases we need to explore in this scenario is 2 4 x 12 x 11 x 10 x 9 190 080 in the following table you can see how many cases can optimally be solved in a certain number of moves both in face turn metric and quarter turn metric face turn metric quarter turn metric depth cases distribution cummulative 0 1 0 00 0 01 1 15 0 01 0 01 2 158 0 08 0 09 3 1 394 0 73 0 82 4 9 809 5 16 5 99 5 46 381 24 40 30 39 6 97 254 51 16 81 55 7 34 966 18 40 99 95 8 102 0 05 100 00 depth cases distribution cummulative 0 1 0 00 0 01 1 10 0 01 0 01 2 73 0 04 0 04 3 500 0 26 0 31 4 3 078 1 62 1 93 5 15 528 8 17 10 10 6 57 180 30 08 40 18 7 91 654 48 22 88 40 8 21 849 11 49 99 89 9 207 0 11 100 00 average 5 81 moves average 6 59 moves the scrambles for the 102 worst cases that require 8 moves to solve in face turn metric can be found here the cross solution for the fixed cross is also listed for each scramble opposite color cross solving when solving the cross on either of two opposite faces there are 8 edge pieces that we need to take into account they can each be oriented in 2 ways and can placed in 12 locations the amount of cases we need to explore in this scenario is 2 8 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 5 109 350 400 in the following table you can see how many cases can optimally be solved in a certain number of moves both in face turn metric and quarter turn metric face turn metric quarter turn metric depth cases distribution cummulative 0 53 759 0 00 0 01 1 806 253 0 02 0 02 2 8 484 602 0 17 0 18 3 74 437 062 1 46 1 64 4 506 855 983 9 92 11 56 5 2 031 420 585 39 76 51 32 6 2 311 536 662 45 24 96 56 7 175 751 822 3 44 99 99 8 3 672 0 00 100 00 depth cases distribution cummulative 0 53 759 0 00 0 01 1 537 496 0 01 0 01 2 3 920 873 0 08 0 09 3 26 775 612 0 52 0 61 4 162 620 494 3 18 3 80 5 773 798 728 15 14 18 94 6 2 260 615 130 44 24 63 18 7 1 794 284 224 35 12 98 30 8 86 731 327 1 70 99 99 9 12 757 0 00 100 00 average 5 39 moves average 6 15 moves the scrambles for the 3672 worst cases that require 8 moves to solve in face turn metric can be found here the cross solutions for the 2 opposite crosses are also listed for each scramble color neutral cross solving when solving the cross on any of the six faces there are 12 edge pieces that we need to take into account they can each be oriented in 2 ways and can placed in 12 locations however since we are using all the edge pieces and edge pieces can only be flipped in pairs the orientation of the 12th edge can be derived from the orientation all the others the amount of cases we need to explore in this scenario is 2 11 x 12 980 995 276 800 in the following table you can see how many cases can optimally be solved in a certain number of moves both in face turn metric and quarter turn metric face turn metric quarter turn metric depth cases distribution cummulative 0 30 942 374 0 00 0 01 1 462 820 266 0 05 0 05 2 4 839 379 314 0 49 0 54 3 41 131 207 644 4 19 4 74 4 239 671 237 081 24 43 29 17 5 543 580 917 185 55 41 84 58 6 151 019 930 400 15 39 99 97 7 258 842 496 0 03 99 99 8 40 0 00 100 00 depth cases distribution cummulative 0 30 942 374 0 00 0 01 1 308 828 676 0 03 0 03 2 2 244 689 022 0 23 0 26 3 15 116 501 844 1 54 1 80 4 86 723 043 456 8 84 10 64 5 333 077 773 019 33 95 44 60 6 475 482 906 734 48 47 93 07 7 67 953 971 216 6 93 99 99 8 56 619 244 0 01 99 99 9 1 215 0 00 100 00 average 4 81 moves average 5 50 moves the scrambles for the 40 worst cases that require 8 moves to solve in face turn metric can be found here the cross solutions for all 6 possible crosses are also listed for each scramble this page is maintained by lars vandenbergh last update on 26th may 2026