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You roll 100 fair six-sided dice. Whenever the results contain at least one occurrence of each value in {1,2,3,4,5,6}, you remove one complete set {1,2,3,4,5,6} from the roll. You repeat this procedure as long as at least one full set can be removed. What is the expected number of dice remaining once no more complete sets can be removed?
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Quantitative Researcher (Intern)

Interviewed at Squarepoint Capital

3.9★
Nov 28, 2025

You roll 100 fair six-sided dice. Whenever the results contain at least one occurrence of each value in {1,2,3,4,5,6}, you remove one complete set {1,2,3,4,5,6} from the roll. You repeat this procedure as long as at least one full set can be removed. What is the expected number of dice remaining once no more complete sets can be removed?

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