HMMT 2012 U7

Guts
Answer

$M$ is an $8 \times 8$ matrix. For $1 \leq i \leq 8$ , all entries in row $i$ are at least $i$ , and all entries on column $i$ are at least $i$ . What is the minimum possible sum of the entries of $M$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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