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Bundeswettbewerb Mathematik 1987 Problem 1.4

Source: Bundeswettbewerb Mathematik 1987 Round 1

October 9, 2022
geometry3D geometrycombinatoricsDifferencecubeGeneralization

Problem Statement

Place the integers 1,2,…,n31,2 , \ldots, n^{3} in the cells of a n×n×nn\times n \times n cube such that every number appears once. For any possible enumeration, write down the maximal difference between any two adjacent cells (adjacent means having a common vertex). What is the minimal number noted down?
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