The Most Intelligent Prince

1. The Most Intelligent Prince

A king wants his daughter to marry the smartest of 3 extremely intelligent young princes, and so the king's wise men 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 king tells them that the first prince to deduce the color of his 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 prince's heads. After some time you realize that the other prince's are unable to deduce the color of their hat, or are unwilling to guess. What color is your hat?

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

Added 1 January 2007

Show Hint Show Solution

Hint:

Based on what you know, why are the other princes unable to solve this puzzle?

Solution:

White.

The king would not select two white hats and one black hat. This would mean two princes would see one black hat and one white hat. You would be at a disadvantage if you were the only prince wearing a black hat.

If you were wearing the black hat, it would not take long for one of the other princes to deduce he was wearing a white hat.

If an intelligent prince saw a white hat and a black hat, he would eventually realize that the king would never select two black hats and one white hat. Any prince seeing two black hats would instantly know he was wearing a white hat. Therefore if a prince can see one black hat, he can work out he is wearing white.

Therefore the only fair test is for all three princes to be wearing white hats. After waiting some time just to be sure, you can safely assert you are wearing a white hat.

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Comments (28)

Anonymous 5 February 2008

I cannot deduce how the solution is 4 for 'The Most Intelligent Prince'. Can you please explain?

Anonymous 22 April 2008

Can I know the answer to The Most Intelligent Prince?

Anonymous 22 May 2008

The solution for 'The Most Intelligent Prince' does not open. Can you fix this issue?

Anonymous 7 September 2008

The solution for the puzzle 'The Most Intelligent Prince' is not appearing on the website.

Anonymous 17 December 2008

I can't access the answer for 'The Most Intelligent Prince'. Can you help me with this?

Anonymous 25 January 2009

The solution for 'The Most Intelligent Prince' problem does not reveal when the solution button is clicked. Could you please tell me the answer?

Anonymous 25 January 2009

I enjoy your logic problems, but some solutions are not available. For instance, the solution for 'The Most Intelligent Prince' does not reveal anything.

Anonymous 28 January 2009

There is no answer to the 'Most Intelligent Prince' question. How come?

Anonymous 21 February 2009

The 'Show Solution' button is not working on The Most Intelligent Prince. What is the answer?

Anonymous 14 March 2009

I believe the solution for The Most Intelligent Prince is Black Hat.

Anonymous 6 May 2009

There are no solutions available for the difficult questions on the site. Please upload the solutions.

Anonymous 9 May 2009

In 'The Most Intelligent Prince', the solution seems to be inaccessible. I would appreciate it if you could provide the answer directly or fix the link to the solution.

Anonymous 27 May 2009

I believe the answer to The Most Intelligent Prince is white.

Anonymous 3 September 2009

The solution link for The Most Intelligent Prince puzzle is broken.

Anonymous 13 September 2010

The math behind some of these puzzles is completely wrong.

Anonymous 11 April 2011

The fireman puzzle took me 50 minutes to figure out!

Anonymous 27 May 2012

The prince problem lacks a good answer. If they all saw the same thing, they would logically come to the same conclusion.

Anonymous 11 September 2012

My problem is not with the solution of The Most Intelligent Prince, but with your reasoning. This is an example in Game theory, and you can deduce you wear a white hat based on the reasoning of what the other princes see.

Anonymous 11 September 2012

Your reasoning about the hat colors in 'The Most Intelligent Prince' is insightful. It highlights the game theory aspect that is often overlooked.

Anonymous 25 November 2012

The text solution for 'The Most Intelligent Prince' does not match the numerical solution provided.

Anonymous 20 December 2012

The last answer is incorrect. If you ask someone if they have a dollar and they actually have two dollars, they will still respond affirmatively.

Anonymous 21 February 2013

The solution to 'The Most Intelligent Prince' is flawed. The hint about fairness is misleading, as it suggests the prince has either one white hat or two black hats, which confuses the odds.

Anonymous 23 August 2013

There is a logical problem with The Most Intelligent Prince puzzle. You claim the answer is White, but if you have a black hat on, the other princes would see a black and a white hat, so their guess for the color of their own hat would not be certain.

Anonymous 23 August 2013

The reasoning for the answer being White in 'The Most Intelligent Prince' puzzle is flawed; the other princes cannot logically deduce their hat colors.

Anonymous 17 June 2015

For the puzzle The Most Intelligent Prince, the answer is right (white) but the reasoning is wrong. If I were wearing a black hat, then the other princes would see me and think about their own hats.

Anonymous 17 June 2015

The reasoning for the answer in 'The Most Intelligent Prince' seems incorrect. If A sees B and C wearing white hats, he would deduce that if he were wearing a black hat, B would conclude he is wearing white after seeing C's hat. Since B doesn't say anything, A concludes he must be wearing a white hat.

Anonymous 1 December 2017

The answer to The Most Intelligent Prince puzzle is wrong. The original problem states the test has to be fair for all princes. If the king was bound by fairness, he couldn't use any black hats at all.

Anonymous 1 December 2017

I first heard about 'The Most Intelligent Prince' puzzle 50 years ago, and I know the answer. However, I cannot access your solution when I click on it.

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