Problem #5
3 Musketeers
There are 3 people A, B and C. Three of them have positive integers written on their hats. One can only see the numbers written on others hats and can not see the number written on his own hat. The number on one of the hats is the sum of the numbers on the other 2 hats. Now the following event occurs
- A was asked about the number on his hat. He replies "Don't know".
- B was asked about the number on his hat. He also replies "Don't know".
- C was asked about the number on his hat. He also replies "Don't know".
- A was asked again the number on his hat. He replies "65".
Find the product of the three numbers on the hats.