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2016 CNMO Grade 10/11 P4

Source: 2016 China Northern MO Grade 10, Problem 4; 2016 China Northern MO Grade 11, Problem 4

February 24, 2020
combinatorics

Problem Statement

Can we put intengers 1,2,⋯ ,121,2,\cdots,12 on a circle, number them a1,a2,⋯ ,a12a_1,a_2,\cdots,a_{12} in order. For any 1≤i<j≤121\leq i<j\leq12, ∣ai−aj∣≠∣i−j∣|a_i-a_j|\neq|i-j|?
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