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Twice meaner

Source: Kyiv City MO 2024 Round 1, Problem 11.1

January 28, 2024
algebramean

Problem Statement

Four positive integers a,b,c,da, b, c, d satisfy the condition: a<b<c<da < b < c < d. For what smallest possible value of dd could the following condition be true: the arithmetic mean of numbers a,b,ca, b, c is twice smaller than the arithmetic mean of numbers a,b,c,da, b, c, d?
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