Once upon a time, there was a powerful kingdom with a powerful king. This king had a lust for popularity, a lust for power, and a lust to be loved by all. Unfortunately for the king, his people did not look up to him. Rather, in times of need, they looked to the 4 wise men who lived in his lands. It was generally accepted that the wise men were smarter than the king, and this bothered the king greatly.
Normally, the king could simply order that they be put to death. However, he knew that this would greatly upset the people. He decided to come up with a plan to outsmart the wise men, proving that they were not as wise as the people believed. After embarrassing them publicly with a problem they could not solve, he knew the people would more readily accept his decision to end their lives.
The king ordered stands to be built in his courtyard, as well as a solid brick wall in the center. He then called for the wise men and had them placed in the following positions. They were each told of their position:
The king then said the following:
You are here today because you claim to be the wisest of all men, but I am going to prove you wrong with a test. You will each be blindfolded shortly. While you are blindfolded, a hat will be placed upon each of your heads. There are exactly 2 red hats and 2 green hats. Once the hats are on your heads, the blindfold will be removed. You will not be able to see the color of the hat on your own head, nor will you be able to see the color of the hat on the person behind you. You must face forward at all times and may not move or turn. To make this even more difficult, one of you will be separated by a brick wall so that you can not see the others and they can not see you. You may not speak or communicate in any way, except to answer my question….
The king then had the hats put on them in this way:
The king continued to speak:
The question that any one of you must answer is “what color hat do you have on?”. Only one of you may answer. If you answer correctly, you all live. If you answer incorrectly, you all die. Remember, you may not speak, move, or otherwise communicate except to answer my question. Also remember that there are exactly 2 green hats and exactly 2 red hats. Take all the time you need.
After a short time, one of the wise men answered. He was certain of his answer, and was correct. The king, baffled at the incredible intelligence was forced to let them all go.
Now your questions are as follows:
- Who answered?
- How did they know the color of their hat?
THE ANSWER IS BELOW
Tip #1: Think about what they can each see.
Answer to Tip #1: Wise man #1 can’t see anything. Neither can #2. Wise man #3 can see the person in front of him, and Wise man #4 can see both of the people in front of him.
Tip #2: If they were each to *guess* based on the odds, what would each of them guess?
Answer to Tip #2: Wise man #1 and #2 cannot see anything at all, so they have a 50% chance of being either green or red. Wise man #3 sees a green hat in front of him. He therefore knows that there is 1 green hat left, and 2 red hats left. Based on those odds, there’s a 66% chance that he is red. Wise man #4 sees both a green hat and a red hat in front of him. Since there is 1 green hat and 1 red hat left, his chances are being either are 50%.
Tip #3 (PART OF THE ANSWER): Wise man #3 is the one who answers. In this case, he says “RED”. Of course, he is correct. No, he wasn’t guessing. So how did he know?
Tip #4: Remember, he didn’t answer right away. It says that “after a short time, one of them answered”. Why didn’t he answer right away?
Tip #5: Only Wise man #3 and #4 could see anything. What are the possible combinations based upon what they can see?
The one thing that Wise man #3 and #4 have in common is that they both see that Wise man #2 is green. After waiting a short time, Wise man #3 knows that he can not be green. If he were, this would be the only possible combination (with 2 red hats and 2 green hats):
If that were the case, Wise man #4 would have seen 2 green hats, and since there are ONLY 2 green hats, Wise man #4 would have answered RED. Basically, if #2 and #3 were the same color, #4 would answer the opposite color.
Because #4 did not answer, #3 knew that he had to be the opposite color of #2, so he was able to confidently answer correctly!