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China MO 2023 P4

Source: China MO 2023 P4

December 30, 2022
combinatorics

Problem Statement

Find the minimum positive integer n≥3n\ge 3, such that there exist nn points A1,A2,⋯ ,AnA_1,A_2,\cdots, A_n satisfying no three points are collinear and for any 1≤i≤n1\le i\le n, there exist 1≤j≤n(j≠i)1\le j \le n (j\neq i), segment AjAj+1A_jA_{j+1} pass through the midpoint of segment AiAi+1A_iA_{i+1}, where An+1=A1A_{n+1}=A_1
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