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I came upon a question that I was struggling on.

The question is:

A teacher has five cards, labelled 1,2,3,4,5. The teacher then takes two cards from the five cards, a gives them to two people.

The teacher then asks the first person:

Is your card number larger than the second person?

The person responded:

I don't know.

The teacher then asked the second person:

Is your card number larger than the first person?

This person responded:

I don't know.

The teacher then told the class:

What is the value of the second person's card?

Someone answered it correctly. What is the number?

What I know

If both people had either 1 or 5 on their cards, then they would have said:

No

or

Yes

So that means we can eliminate 1 and 5, so the second person must have had 2,3,4.

Problem

How do we get to the conclusion that the second person has 2,3 or 4?

Stevo
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1 Answers1

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Person $2$ doesn't have $1$ or $5$, and he can deduce that person $1$ does not. If he had $4$, he'd know he had the higher card, and if he had $2$, he'd know he had the lower card.

The second person's card is $3$.

saulspatz
  • 53,131