28 Jan '08 13:01

We have a square divided into n^2 small identical squares.

1: Draw an "X" in n-1 of the little squares.

2: If there is an empty little square which has at least 2 neighbors with an "X" in them, you may draw an "X" in this square. Two little squares are neighbors if they have a common edge.

3: Return to step 2, until there are no more empty little squares which have at least 2 neighbors with an "X" in them.

PROVE:

it is not possible that all n^2 little squares will get an "X".

1: Draw an "X" in n-1 of the little squares.

2: If there is an empty little square which has at least 2 neighbors with an "X" in them, you may draw an "X" in this square. Two little squares are neighbors if they have a common edge.

3: Return to step 2, until there are no more empty little squares which have at least 2 neighbors with an "X" in them.

PROVE:

it is not possible that all n^2 little squares will get an "X".