Cube Mystery Cache
-
Difficulty:
-
-
Terrain:
-
Size: 
(regular)
Please note Use of geocaching.com services is subject to the terms and conditions
in our disclaimer.
Widely used in schools and universities to help explain complex
particle physics and mathematical algorithms. There are 6 colored
sides, 21 pieces and 54 outer surfaces. The total number of
possible configurations is calculated by multiplying the number of
possible arrangements of the corner pieces by the number of
possible arrangements of edge pieces. There are 8 corner pieces, so
the number of possible arrangements equals 8! (or 8x7x6x5x4x3x2x1),
which is 40320. Each corner piece has 3 different orientations, so
this figure must be multiplied by 38 (3x3x3x3x3x3x3x3), which
equals 6561. But when almost complete, the number of possible moves
diminishes, so the equation must be adjusted. In this case, once
the second from last corner piece is placed, the last piece can
have only one automatic orientation, so 6561 must be divided by 37,
which is 2187. Finally, the total possible arrangements of corner
pieces 40320 x 2187 = 88,179,840.
With the 12 Edge Pieces, the number of possible arrangements
equals 12! (12x11x10…), which is 479,001,600. However, unlike
corner pieces, it is impossible to exchange just two edge pieces,
so once the third from last is placed, the remaining two can have
only one possible arrangement, which means this figure must be
divided by 2, leaving 239,500,800. Each edge piece has two
different orientations, so this must now be multiplied by 212,
which gives 6561. This figure must also be adjusted because once
the third from last edge piece is placed, one of the remaining two
can be reoriented but the last will always have a fixed orientation
in relation to it. So 6561 must be divided by 211, which is 2048.
Finally, the total possible arrangements of edge pieces 239,500,800
x 2048 = 490,497,638,400.
But there is only one solution which you must solve at the first
stage to reach the final. This two part multi could be easy for
some but difficult and frustrating (including myself) for others. I
have tried to place this in a muggle free area. However, Stuff
happens! If you should encounter muggles please be discreet as I do
not have a back-up for this cache. Careful of mosquitoes, bugs,
ants and stuff.
Additional Hints
(Decrypt)
First Stage: Oebxra Cvar
Final: Ovt Cvar