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?
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 $3$.