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Please read question of distinct permutation matrices with rotation at first, then new counting questions are below:

  1. For a distinct $N\times N$ zero-symmetry permutation matrix, we could rotate it 3 times and imprint all 4 images into a single canvas. Then there would be at most $4\times N$ cells selected in the final imprinted matrix. I called such matrix is Dispersed. How many Dispersed matrices for $N\times N$ permutation matrices?

  2. In the set of above imprinted matrices, some are same. Then how many distinct imprinted matrices?

Some examples of imprinted images for $4\times 4$ matrices (Please only look at row 2,3,5 and 6 which are zero-symmetry matrices. The images in left side are original, and in right side are imprinted ones. In special, images in row 5 and 6 are Dispersed):

enter image description here

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Is this question really so hard? –  gnozil Jun 26 '12 at 7:38

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