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NL-NWO 2015 Problem 2

    On a 1000×10001000\times 1000 -board we put dominoes, in such a way that each domino covers exactly two squares on the board. Moreover, two dominoes are not allowed to be adjacent, but are allowed to touch in a vertex. Determine the maximum number of dominoes that we can put on the board in this way.

    Attention: you have to really prove that a greater number of dominoes is impossible.

    Dataset text AI-MO AoPS. Quoted with source.

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