Three prisoners in deathrow are put together. They each get a unique number on their forehead. They are NOT allowed to speak to each other, only to their guard. They only get 2 clues:
- The number on their head is always higher than zero
- One of the numbers is the total of the other two numbers.
If they can guess their numbers, they are free to go.
- Person 1 gets asked if he knows his number. He says he doesn't.
- Person 2 gets asked the same, but also replies that he doesn't know
- Person 3 is being asked but doesn't know either.
Since none of them answered wrong. They get another chance.
- Person 1 again doesn't know.
- Person 2 also doesn't know.
- Person 3 however does know the answer this time: It's 148 on his head. This answer is correct and he is allowed to leave.
Question: What are the numbers on the heads of person 1 and 2 and how does person 3 know his own number?