Logic Puzzles from multiple points of view 4/5
July 3, 2009 pm31 1:15 pm
Over the next few days I’ll be posting a group of five puzzles, related by a “multiple points of view” theme.
None of these puzzles belong to me. And I don’t know where to extend credit. I think they’ve just sort of existed, forever.
Prisoners with Hats
Three perfectly logical prisoners are seated facing each other, with hats on their heads. Each hat has a counting number {1, 2, 3, 4, …} on it, and each prisoner can see the hat of the other two prisoners, but not his own.
The warden says,
- I will set free the man who can tell me his own number, but execute any man guessing incorrectly.
They look back at him in stunned silence.
- “OK, a hint. One of your numbers is the sum of the two. Alan?”
- I don’t know my number.
- Bert?
- I don’t know my number.
- Graham?
- I don’t know my number.
- Alan?
- I still don’t know my number.
- Bert?
- My number is 26.″
And he went free. What were Alan and Graham’s numbers? Explain your reasoning. Why did it take five questions to get an answer?
Place questions/clarifications below. To submit proposed solutions, click here.
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