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positive integrs in 9x9 grid

Source: 2024 Mathematics Regional Olympiad of Mexico West P3

October 21, 2024
combinatorics

Problem Statement

In each box of a 9×99\times 9 grid we write a positive integer such that, between any 22 boxes on the same row or column that have the same number nn written, there's at least nn boxes between them. What is the minimum sum possible for the numbers on the grid?
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