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I have this as an exercise but I'm not sure what's the best way to approach it. I've tried the pack them but wasn't able to do so. I see that having them combined will yield in 10 whites and 10 blacks ( because every piece will cover 2 blacks and 2 whites) which is exactly the chessboard but not sure if that's it.

the exercise

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every piece will cover 2 blacks and 2 whites

Are you sure about that? Have another look before looking at the spoiler below.

The T piece will cover 1 black and 3 white (or 3 black and 1 white). Every other piece covers 2 black and 2 white. So in total they will cover 9 black and 11 white (or 11 black and 9 white). Since the board have 10 black and 10 white, it is not possible.

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This one is simple.

It is not possible to cover the 5x4 board with the given tetrominoes because

The total number of cells is $20$, $10$ black and $10$ white.

All cover $2$ black and $2$ white cells. Except one

solution


That one, covers either 1 black and 3 white or 1 white and 3 black. Since, the counts comes to $8+1$ for black and $8+3$ for white (or vice-verse). We would never have all $10$ white and all $10$ black cells covered.

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