# Numbered Hats

Alice, Bob, and Charlie, three perfect logicians, are sitting in a circle, when Eve comes and places a hat on each of their heads, with a number on each hat facing so that each logician can see the numbers of the other two, but not their own. They are then publicly told that each of them was given a positive (non-zero) whole number, and two of their numbers add up to the third.

The following dialog takes place.

Alice: I can't determine the number on my head. Bob: I can't determine the number on my head. Charlie: I can't determine the number on my head. Alice: I was able to determine the number on my head is 50!

What numbers do Bob and Charlie have? Your solution should be Bob's number followed by Charlie's number, separated by a space.

#### Attempt Info

- Correct Attempts: 10
- Incorrect Attempts: 12
- Ungraded Attempts: 0
- Total Attempts: 22