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A difficult combinatorics problem with a (cute?) animal

Source: Germany 2003 - Problem 3

December 26, 2022
combinatoricssquareboardwayweightsgrid

Problem Statement

Consider a N×NN\times N square board where N≥3N\geq 3 is an odd integer. The caterpillar Carl sits at the center of the square; all other cells contain distinct positive integers. An integer nn weights 1\slash n kilograms. Carl wants to leave the board but can eat at most 22 kilograms. Determine whether Carl can always find a way out when a) N=2003.N=2003. b) NN is an arbitrary odd integer.
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