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Omni-MATH / Let n and k be positive integers such that (1)/(2)n<k≤(2)/(3)n. Find the least number m for which it is possible to place m pawns on m squares of an n×n chessboard so that no colum…

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problem

Let n n and k k be positive integers such that 12n<k≤23n. \frac{1}{2} n < k \leq \frac{2}{3} n. Find the least number m m for which it is possible to place m m pawns on m m squares of an n×n n \times n chessboard so that no column or row contains a block of k k adjacent unoccupied squares.
Plain-text mathematical notation (without MathML)
Let n and k be positive integers such that (1)/(2)n<k≤(2)/(3)n. Find the least number m for which it is possible to place m pawns on m squares of an n×n chessboard so that no column or row contains a block of k adjacent unoccupied squares.
Original LaTeX notation
Let $ n$ and $ k$ be positive integers such that $ \frac{1}{2} n < k \leq \frac{2}{3} n.$ Find the least number $ m$ for which it is possible to place $ m$ pawns on $ m$ squares of an $ n \times n$ chessboard so that no column or row contains a block of $ k$ adjacent unoccupied squares.

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Source and history

task_id
693ba4aa-1522-547f-b745-3f404e1c80b3
task_key
test--693ba4aa-1522-547f-b745-3f404e1c80b3
task_revision_id
1
config / split
/ test

Official source

initial import