olymmath

HMMT November 2018 U23

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Let SS be a subset with four elements chosen from {1,2,…,10}\{1,2, \ldots, 10\}. Michael notes that there is a way to label the vertices of a square with elements from SS such that no two vertices have the same label, and the labels adjacent to any side of the square differ by at least 4 . How many possibilities are there for the subset SS ?

Dataset text NuminaMath olympiads. Quoted with source.

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