spyr0th3dr4g0n
Member
I plotted the natural log of the number of states per moves to solve, and got a nice trend.
Taking data from this site for the 2x2x2
Taking data from cube20 and making a similar plot
We can see from the graph that the 3x3x3 approximations look like they might underestimate 16 moves and over estimate 18 moves, but they are otherwise fairly accurate.
Plotting using the same function for 2x2x2 htm gives a similar looking curve.
Is there any reason this trend shouldn't continue for higher order cubes? Is there any data for the number of states per optimal moves to solve for 4x4x4 cubes?
Taking data from this site for the 2x2x2
Taking data from cube20 and making a similar plot
We can see from the graph that the 3x3x3 approximations look like they might underestimate 16 moves and over estimate 18 moves, but they are otherwise fairly accurate.
Plotting using the same function for 2x2x2 htm gives a similar looking curve.
Is there any reason this trend shouldn't continue for higher order cubes? Is there any data for the number of states per optimal moves to solve for 4x4x4 cubes?
Code:
0 1 0
1 6 1.791759469
2 27 3.295836866
3 120 4.787491743
4 534 6.280395839
5 2256 7.721348613
6 8969 9.101529466
7 33058 10.40601887
8 114149 11.64525989
9 360508 12.79526943
10 930588 13.74357192
11 1350852 14.11624606
12 782536 13.57029521
13 90280 11.41067123
14 276 5.620400866
Code:
0 1 0
1 18 2.890371758
2 243 5.493061443
3 3240 8.083328609
4 43239 10.67449814
5 574908 13.26196531
6 7618438 15.84608192
7 100803036 18.42867903
8 1332343288 21.0102051
9 17596479795 23.59096471
10 2.32248E+11 26.17107188
11 3.06329E+12 28.75051023
12 4.03744E+13 31.32921767
13 5.31653E+14 33.90701292
14 6.98932E+15 36.48315975
15 9.13651E+16 39.05364047
16 1.1E+18 41.54184185
17 1.2E+19 43.93143832
18 2.9E+19 44.8138275
19 1.5E+18 41.85199678
20 490000000 20.00991595