| Author |
Message |
Greg Schmidt (Gschmidt)
| | Posted on Thursday, December 22, 2005 - 11:06 am: | |
Here are the results of some analysis I performed on the "Rotation Squares" puzzle.
There are 262,144 possible patterns, not including reflections or rotations. Divide that number by the eight possible symmetries of the square to obtain 32,768 unique configurations.
The diameter of the permutation group is 18 which is another way of saying that the minimum number of moves required to reach any pattern is less than or equal to 18. It turns out that there is a single "maximal" pattern that is 18 moves away from the start pattern.
The number of patterns (not including rotations and reflections) is given below along with the minimum number of moves required to achieve that pattern.
e.g. f(3) = 816 is read as "there are 816 patterns at a distance of 3 moves from start".
f(0) =1
f(1) =18
f(2) =153
f(3) =816
f(4) =3060
f(5) =8568
f(6) =18564
f(7) =31824
f(8) =43758
f(9) =48620
f(10)=43758
f(11)=31824
f(12)=18564
f(13)=8568
f(14)=3060
f(15)=816
f(16)=153
f(17)=18
f(18)=1 |
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