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numbers 1-121 in 11x11 All-Russian MO 1995 Regional (R4) 9.8

Source:

August 26, 2024
combinatorics

Problem Statement

Can the numbers 1,2,...,1211,2,...,121 be written in the cells of an 11×1111\times 11 board in such a way that any two consecutive numbers are in adjacent cells (sharing a side), and all perfect squares are in the same column?
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