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n numbers in a circle, digits - All-Russian MO 1999 Regional (R4) 9.1

Source:

September 25, 2024
number theoryDigits

Problem Statement

All natural numbers from 11 to NN, N2 N \ge 2 are written out in a certain order in a circle. Moreover, for any pair of neighboring numbers there is at least one digit appearing in the decimal notation of each of them. Find the smallest possible value of NN.