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cube

open up the cube such that:
    _
_|_|_
|_|_|_|
  |_|
  |_|

now Place 1 color at the centre (cross- intersection)

so you have 5 flaps and 5 colors to place in them...so 5 choices of colors in the 1st flap...4 in 2nd...3 in 3rd...2in 4th and 1 color left for the last.....or simply 5!= 5x4x3x2x1=120.......

Note:The 4 flaps just adjacent to the centre have rotational symmetry so a particular combination of colors has 4 places to start from  ... and when rotated about the centre gives the same cube...since the bottom most flap is touching each 4 of them (when this development is folded back into the cube)

so we have to divide by 4 hence the answer is 5!/4=  30 distinguished cubes

Pushkar Awasthi
Monday, January 17, 2005

Just found it easier to visuallise this way although the solution has the same concept as Erick C. Jone's..which is better written

Pushkar Awasthi
Monday, January 17, 2005

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