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n numbers 1s and 2s in a circle - All-Russian MO 2001 Regional (R4) 8.2

Source:

September 25, 2024
algebranumber theory

Problem Statement

NN numbers - ones and twos - are arranged in a circle. We mean a number formed by several digits arranged in a row (clockwise or counterclockwise). For what is the smallest value of NN, all four-digit numbers whose writing contains only numbers 11 and 22, could they be among those shown?