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Omni-MATH / We consider an n×n table, with n≥1. Aya wishes to color k cells of this table so that that there is a unique way to place n tokens on colored squares without two tokens are not in …

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problem

We consider an n×nn \times n table, with n≥1n\ge1. Aya wishes to color kk cells of this table so that that there is a unique way to place nn tokens on colored squares without two tokens are not in the same row or column. What is the maximum value of kk for which Aya's wish is achievable?
Plain-text mathematical notation (without MathML)
We consider an n×n table, with n≥1. Aya wishes to color k cells of this table so that that there is a unique way to place n tokens on colored squares without two tokens are not in the same row or column. What is the maximum value of k for which Aya's wish is achievable?
Original LaTeX notation
We consider an $n \times n$ table, with $n\ge1$. Aya wishes to color $k$ cells of this table so that that there is a unique way to place $n$ tokens on colored squares without two tokens are not in the same row or column. What is the maximum value of $k$ for which Aya's wish is achievable?

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Source and history

task_id
637ef67a-4ec1-577a-be89-c155a6a6c526
task_key
test--637ef67a-4ec1-577a-be89-c155a6a6c526
task_revision_id
1
config / split
/ test

Official source

initial import