Hat Problem
[Here’s my take on the Hat Problem, collating a couple of different problems.]
Three brilliant mathematicians have been kidnapped by Dr Evil, who is forcing them to play the Hat Game! He lines them up, blindfolded, one after the other, facing a wall, so that C can see B and A, B can see A, and A can see nothing:
| A B C
He explains (despite Scott’s protests…) that he has two white hats and three blacks, which he will put on the mathematicians. And, he promises to let them go if at least one person can guess their hat colour correctly. But, he warns them, if anyone guesses incorrectly, he’ll have them all killed anyway.
Version 1:
Simply put, will the mathematicians be able to escape? How should Dr Evil arrange the hats?
Version 2 (leading questions):
When he removes the blindfolds, mathematician C quickly pipes up his hat colour. What was it?
Dr Evil, thinking it could just have been a lucky guess, blindfolds them again and gives them new hats. This time, when he takes off the blindfolds, there’s a pause - and suddenly mathematician B announces his hat colour. What was it?
Frustrated, Dr Evil blindfolds them again and changes the hats. Whipping off their blindfolds, he giggles evilly while they sit silently. Then, mathematician A happily announces his hat colour. What was it?
(Just for the record, Dr Evil threw them all into a pool of sharks with laser beams on their heads anyway.)
rajiv Says:
yes all mathe maticians may say black
it is a very easy question might be something misssing in the queston
Neil Says:
Here’s my answer:
If C can see two white hats in front of him, he can say “my hat is black”. Otherwise he stays silent.
If B sees that A has a black hat, he stays silent. If he sees a white hat, he waits for C to say something. If C doesn’t say anything, B knows that his hat and A’s hat can’t both be white - so he can say “my hat is black”.
A waits for either B or C to say something. If neither of them do, he can say “my hat is black”.
Is there something missing in your description of version 1?
All mathematicians guess black. At least one of them must be right.
Oh, yes, you’re right - I should have put (and now have) in the main text: “But if anyone guesses incorrectly, I’ll have you all killed!”