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a + b + c =? if |a - b| + |b - c| + |c - a| = 1

Source: 2023 South Russian Girls MO - Assara Seniors p5

March 1, 2024
algebra

Problem Statement

Given three non-negative real numbers aa, bb and cc. The sum of the modules of their pairwise differences is equal to 11, i.e. ∣a−b∣+∣b−c∣+∣c−a∣=1|a- b| + |b -c| + |c -a| = 1. What can the sum a+b+ca + b + c be equal to?
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