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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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