Painting a Cube

From 8 8 distinct colors, a cube is painted so that no 2 2 faces sharing a common vertex (adjacent) are painted with same color. If the number of such different colorings possible is N N , find the largest 2 2 digit factor of N N .

This problem is from IOQM (Indian Olympiad Qualifier in Mathematics), I was not able to solve this problem, so a detailed solution would be appreciated.


The answer is 98.

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