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Omni-MATH / Let Q be a (2n+1)×(2n+1) board. Some of its cells are colored black in such a way that every 2×2 board of Q has at most 2 black cells. Find the maximum amount of black cells that t…

Problem

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problem

Let QQ be a (2n+1)×(2n+1)(2n+1) \times (2n+1) board. Some of its cells are colored black in such a way that every 2×22 \times 2 board of QQ has at most 22 black cells. Find the maximum amount of black cells that the board may have.
Plain-text mathematical notation (without MathML)
Let Q be a (2n+1)×(2n+1) board. Some of its cells are colored black in such a way that every 2×2 board of Q has at most 2 black cells. Find the maximum amount of black cells that the board may have.
Original LaTeX notation
Let $Q$ be a $(2n+1) \times (2n+1)$ board. Some of its cells are colored black in such a way that every $2 \times 2$ board of $Q$ has at most $2$ black cells. Find the maximum amount of black cells that the board may have.

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Source and history

task_id
2fdb9114-481c-5ba3-a15c-b174e560c1f6
task_key
test--2fdb9114-481c-5ba3-a15c-b174e560c1f6
task_revision_id
1
config / split
/ test

Official source

initial import