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In how many ways can one put 2 distinguishable objects on a 4x4 board?

In how many ways can one put them so that when you rotate the board to 90 degrees the positions of objects is preserved?

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  • $\begingroup$ Welcome to math.SE! There's no need to repeat the tags in the title; the tags are displayed wherever the title is displayed. The tags are for general fields, whereas the title should be a more specific summary of the question. $\endgroup$
    – joriki
    Oct 14, 2012 at 18:34

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There are $16$ different positions, so there are $16$ options for placing the first object and $15$ options for placing the second, for a total of $16\cdot15=240$.

There is no way to put them such that positions are preserved under rotations of $90^\circ$, even if they were indistinguishable, since no two positions on the board are transformed into each other under such rotations.

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  • $\begingroup$ @Pilot: You're welcome! $\endgroup$
    – joriki
    Oct 14, 2012 at 18:39

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