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There are 6 pieces of white chopsticks, 8 pieces of yellow chopsticks, and 10 pieces of blue chopsticks mixed together. If you want to get 4 pairs of chopsticks with the same colors in dark, at least how many pieces of chopsticks are needed to be taken?

Upon seeing this question, I thought logically that given the worst possible scenario, if I pick out 9 chopsticks then I could get 3 of each type, but as soon as I pick out 10, then I am guaranteed to have at least 4 chopsticks with the same color. However, I am unsure if this thinking is correct or not. Also, how can this be solved using the pigeonhole principle?

Ved Rathi
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Since there exists 3 different colors, you can have at most 3 unpaired chopsticks (by pidgeon hole principle), which means the maximum of chopsticks you can hold while having only 3 pairs of same color is $3\times 2 + 3 = 9$, which means upon adding one more you will have more than 3 pairs.

Zechen Ma
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