Problem

Source: 2022 Taiwan TST Round 1 Independent Study 2-C

Tags: combinatorics, geometry, circumcircle, ming



Let $\triangle P_1P_2P_3$ be an equilateral triangle. For each $n\ge 4$, Mingmingsan can set $P_n$ as the circumcenter or orthocenter of $\triangle P_{n-3}P_{n-2}P_{n-1}$. Find all positive integer $n$ such that Mingmingsan has a strategy to make $P_n$ equals to the circumcenter of $\triangle P_1P_2P_3$. Proposed by Li4 and Untro368.