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numbers 1 - 16 written in the cells of a 4x4 board

Source: Mexican Mathematical Olympiad 1997 OMM P3

July 28, 2018
combinatoricsboard

Problem Statement

The numbers 11 through 1616 are to be written in the cells of a 4×44\times 4 board. (a) Prove that this can be done in such a way that any two numbers in cells that share a side differ by at most 44. (b) Prove that this cannot be done in such a way that any two numbers in cells that share a side differ by at most 33.
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