Ark's Perplexing Puzzles
- Thread starter arkvoodle
- Start date
I knew this one was well known! 10 puzzle points.
Puzzle 005- Princes and Princesses- 15PP
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.
Puzzle 005- Princes and Princesses- 15PP
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.
Eduarda
Srishti is annie is eduarda right?
Black? If I am either one of the other princes, then my competitors will have one black hat and the other one white if my answer is correct, and then I will be more confused than if both the competitors have a white hat. If I'm wrong, I predict the next person to be right! (I can tell the future!) 
- Joined
- Sep 16, 2009
- Location
- Cali For Nuh
well if there are 3 white hats and 2 princes wear white hats... that means there is 1 possible white hat or two possible black hats on his head.
Just with probability there is a 33% his hat is white, and 66 % chance his hat is black. However...
3 white - 1 on one prince head = 2 white hats remaining 66% chance
2 black hats - 1 on one prince's head 33% chance
or...
3 white - 2 on two prince's heads = 1 hat remaining = 33% chance
2 black - 0 on princes head... = 2 hats remaining = 66% chance
Or lets go with this 3rd batch I neglected... until now
Solely based on probability the answer would be black. However there is always still a chance it could be white. Which is why asking the color of one's own hat would resolve the uncertainty
Just with probability there is a 33% his hat is white, and 66 % chance his hat is black. However...
While this would make sense even in our prince's world...Lets imagine it from the other prince's perspective.
3 white - 1 on one prince head = 2 white hats remaining 66% chance
2 black hats - 1 on one prince's head 33% chance
or...
3 white - 2 on two prince's heads = 1 hat remaining = 33% chance
2 black - 0 on princes head... = 2 hats remaining = 66% chance
Or lets go with this 3rd batch I neglected... until now
I could just ask the other two princes' what the color of my hat was, and thus deduce my answer from there. He didnt say the prince's couldn't communicate with each other. Which because they were equally wanting to marry the princess. it is very likely they'd lie to you, so you would take the opposite of their reply. Or perhaps since the king is a man of his word. you ask him what color your hat is. =) yeah going with that... Ask the king to tell you your hat color and recite that back to him and take your prize.
Solely based on probability the answer would be black. However there is always still a chance it could be white. Which is why asking the color of one's own hat would resolve the uncertainty
That's a brilliant analysis, but what is your definite final answer, Black or White?
Ding ding ding!
That is correct!
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.
Total PP gained: 9PP
Next puzzle~~~
Puzzle 006- The Father- 5PP
A mother is 21 years older than her child. In exactly 6 years from now, the mother will be exactly 5 times as old as the child.
Where's the father?
Hazel
A Frog
- Joined
- Feb 19, 2010
- Location
- on my bean bag...
The Child's father is away, he has divorced the mother.
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