Problem E

Secret Numbers

Wakana, Yousef, and Zora are each given a card with a positive integer on it. They cannot see each other’s cards, but are told that the sum of their three numbers is \(14\). They then make the following observations.

Wakana says "I know that Yousef and Zora have different numbers."

Yousef then says "I already knew that all three numbers were different."

Zora then says "I now know what all three of the numbers are."

What number does each person have?