MathDB
Different Colors of Balls

Source: Swiss TST 2019 P10

May 12, 2020
combinatorics

Problem Statement

Let n≥5n \geq 5 be an integer. A shop sells balls in nn different colors. Each of n+1n + 1 children bought three balls with different colors, but no two children bought exactly the same color combination. Show that there are at least two children who bought exactly one ball of the same color.
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