MathDB
Digits on a circle

Source: 239 MO 2024 J3

May 22, 2024
number theorycombinatorics

Problem Statement

There are 169169 non-zero digits written around a circle. Prove that they can be split into 1414 non-empty blocks of consecutive digits so that among the 1414 natural numbers formed by the digits in those blocks, at least 1313 of them are divisible by 1313 (the digits in each block are read in clockwise direction).