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MathNet 2019-part-05 — 184 problems (EN–VI) Question 71

Math Olympiad Vault · MathNet 2019-part-05 — 184 problems (EN–VI)

Question 71

Integers from $1$ to $49$ are placed arbitrarily on a quadratic table formed by $7 \times 7$ squares. Show that one can find a $2 \times 2$ square on the table, formed by $4$ neighboring cells, such that the sum of numbers inside is at least $81$.