Problem

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

Tags: combinatorics



Can we put intengers $1,2,\cdots,12$ on a circle, number them $a_1,a_2,\cdots,a_{12}$ in order. For any $1\leq i<j\leq12$, $|a_i-a_j|\neq|i-j|$?