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What Number Is It?

So there are two students, that play a game with their teacher. They have 10 cards, each card is numbered 1,2,3,...,9,10. And then their teacher gives them two cards that is consecutive. For example, one student gets number 4, the second gets number 5 or 3 (3,4 or 4,5), or if one gets 7, the other gets 8 or 6 (6,7 or 7,8), and so on. They don't know each other's card. After that, they will be asked to guess what number is in their friend's hand.

The game started, the teacher gives them cards.

And then, there is this conversation.

A: I don't know your number.

B: Neither do I.

A: Now I know your number.

What are the possible numbers that is given to them?

2,3 or 8,9

Those conversation only happen if their cards is 2,3 or 8,9.

For example, A gets 9 and B gets 8. A said that he don't know B's card. The only possible card for B is 8 or 10. But then he said that he don't know A's card, which is impossible to say when he gets 10. So the only possibilities left is 8, and A knows it. This also apply on 2,3.



2,3 or 8,9

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Submitted by
Rifqi Ardia Ramadhan
over 6 years ago
Difficulty 2.7 ?