Competition problem — Combinatorics

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Combinatorics Difficulty 5.1 AIME, harder Find the answer

90. In a stationery box, there are 38 watercolor pens of the same size, including 10 white, yellow, and red pens each, as well as 4 blue pens, 2 green pens, and 2 purple pens. How many pens must be taken out to ensure that at least 4 pens of the same color are taken out?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Reference answer: 17

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.