Tessellate S.T.E.M.S. (2019) - Computer Science - School - Set 4 - Subjective Problem 2

The Emperor of Persia wants his daughter to marry the smartest of 3 extremely intelligent young princes, and so the Emperor's wise ministers devised an intelligence test.

The princes are gathered into a room and seated, facing one another, and are shown \(2\) black hats and \(3\) white hats . They are blindfolded, and \(1\) hat is placed on each of their heads, with the remaining hats hidden in a different room.

The Emperor tells them that the first prince to deduce the color of his own hat without removing it or looking at it will marry his daughter. A wrong guess will mean death. The blindfolds are then removed.

You are one of the princes. You see \(2\) white hats on the other princes' heads. After some time you realize that the other princes are unable to deduce the color of their hat, or are unwilling to guess. What color is your hat? Explain how you arrived at the solution.

Note: You know that your competitors are very intelligent and want nothing more than to marry the princess. You also know that the Emperor is a man of his word, and he has said that the test is a fair test of intelligence.


This problem is a part of Tessellate S.T.E.M.S (2019)

Note by Tessellate Stems Computer Science
4 weeks, 1 day ago

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It's white.

If your hat is black, another prince will see one black and one white hat and reason as follows: "If my hat is black, the white-hatted prince will see two black hats and will instantly know his hat is white. He hasn't spoken, so my hat must be white."

No prince has done that yet, so your hat is white.

This assumes some things about deduction speed, of course, but I think it's the intended answer.

Patrick Corn - 2 weeks, 3 days ago

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Yeah, I think it is fair to assume some things about deduction speed.

I was wondering if we can pinpoint what those assumptions are.

Agnishom Chattopadhyay Staff - 1 week ago

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Yeah the deduction speed matters

V i S i o N . - 4 days, 18 hours ago

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It's easy.

Let's say our prince has Black hat then 2nd prince see's one Black and One White hat , in no way he can deduce his color . The 3rd prince see's that seconf prince can't deduce his color so he must have wore a white hat because if he had a blacck hat then he(2nd prince) would had deduced his hat color but we know the 2nnd and 3rd prince can't deduce their hat colour so our prince has white hat.

Voila!

V i S i o N . - 4 days, 18 hours ago

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