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Arranging integers in a circle with 3-digit product of adjacent terms

Source: 2023 Singapore MO Round 2 Junior Q2

July 27, 2023
number theory

Problem Statement

What is the maximum number of integers that can be chosen from 1,2,,991,2,\dots,99 so that the chosen integers can be arranged in a circle with the property that the product of every pair of neighbouring integers is 3-digit number?