# Arranging Objects on a 4x4 Board

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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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.