Multiple choice general knowledge

In ten decks of cards, what is the least amount of cards you must take to be guaranteed at least one four-of-a-kind?

  1. 40

  2. 10

  3. 13

  4. 4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By the pigeonhole principle, in 10 decks there are 40 of each rank. To guarantee four of the same rank, consider the worst case: you draw 3 of each of the 13 ranks (39 cards). The next card (40th) must complete a set. Thus, 40 cards guarantee at least one four-of-a-kind.

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