A semi-infinite chess board (vary from zero to infinity in both dimensions) with counters in the three bottom left squares, as shown in the below figure.

How to move: If the squares above and to the right are free, a counter can be removed and replaced by two counters, one in the square above and one in the square to the right – check below

Prove that it is not possible to leave the three bottom left squares empty.

Find Solution here

How to move: If the squares above and to the right are free, a counter can be removed and replaced by two counters, one in the square above and one in the square to the right – check below

Prove that it is not possible to leave the three bottom left squares empty.

Find Solution here

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