On a 1000×1000-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. combinatoricscombinatorial geometrydominoesmaximum