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Mathematicians' Casino

Puzzle 6: Primes

Difficulty:
Fun:
(based on 23 votes)

Over to your left, you spot the Primes table. Primes is unlike any regular casino game. The dealer draws three from a pool of only eight cards: a red 2, 3, 5 and 7, and a black 2, 3, 5, and 7. She then will lay some number of the rest of the cards face up on the table, and make a true statement. The challenge is to guess whether the three cards in her hand add up to a prime number or not. Are you ready to play?

1. The dealer draws her three cards, then lays two cards on the table: a black 7 and a black 3. She says: "I have fewer than two red cards." Is her hand prime?

 Yes
No
2. The dealer draws her three cards, then lays two cards on the table: a red 2 and a black 2. She says: "Two of the cards in my hand have the same number." Is her hand prime?

Yes
No
3. The dealer draws her three cards, then does not lay any cards on the table. She says, "None of the cards in my hand have the same number." Is her hand prime?

 Yes
No

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