Chessboard Problems.

Algebra Level 4

Jake and Logan play a game on a 2020 × 2020 {2020} \times {2020} chessboard. In the beginning the board is empty. In every turn, Logan places a black knight on an empty square in such a way that his new knight does not attack any previous knights. Then Jake places a white queen on an empty square. The game gets finished when somebody cannot move.

Find the maximal positive K K such that, regardless of the strategy of Jake, Logan can put at least K K knights on the board.


The answer is 1020100.

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