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two 2s and two 24s on a 13 x13 board , integers in adjacent cells differ by 1

Source: 2018 Saudi Arabia GMO TST I p4

July 31, 2020
combinatoricssquare board

Problem Statement

In each of the cells of a 13×1313 \times 13 board is written an integer such that the integers in adjacent cells differ by 11. If there are two 22s and two 2424s on this board, how many 1313s can there be?
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