self Maths Puzzle

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

Read Solution (Total 1)

Forty.

The number of decks is irrelevant; the answer is the same if one or one-hundred decks are used.

Any card drawn will be a A,2,3,4,5,6,7,8,9,10,J,Q, or K, so there are 13 possibilities each time a card is drawn.

The fastest way to draw a four of a kind is if the first four cards all have the same "value." The slowest way, which provides the solution, is to first draw 13 three of a kinds, and then one more card.

Since 13 x 3 + 1 = 40, if 40 cards are drawn it is guaranteed that those forty cards contain at least one four of a kind.
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self Other Question

A man has four cards in his hand facing him, from 2 to 5. He wants them placed in ascending order from his left to his right. To do this, he takes the leftmost card (from your perspective) and puts it last. He then takes the third card from the right (your right) and puts it in last place.

What was the previous order of the cards? On your travels you come to an old man on the side of the road holding three cards from a standard deck face down. Trying to make conversation you ask him what the three cards are.

He tells you, "To the left of the queen, are one or two jacks. To the right of the jack, are one or two jacks. To the right of the club, are one or two diamonds. To the left of the diamond, are one or two diamonds." What are the three cards?