Riddles have intrigued us for a long time and maybe that’s the reason why we continue to create more and more riddles. Though we create new and interesting ones from time to time, there are some that always spark the curiosity of each generation and even causes frustration sometimes. Here’s one type of induction puzzle that is known as the prisoner’s hat riddle that is around some quite some time now.
What exactly is the riddle?
This riddle includes 4 prisoners and 4 hats. Although there are many variants of this riddle now, the overall setting is the same. So one day these four prisoners are outside of their cells doing some work under the prisoner work program and for some reason, the warden asks them to play a game and says if they win, they are free from the jail. Of course, they all agree.
In some variation of this riddle, prisoners are buried up to their neck in others they are stood up on a box. Either way, 3 of these prisoners are in line while the fourth prisoner is behind a wall that is quite big. So let’s call them A, B, C, and D. Prisoner A is behind prisoner B and prisoner B is behind prisoner C, then there is a wall in front of prisoner C and behind the wall is prisoner D, also prisoner C and D are facing the wall. Here, Prisoner A can see prisoner B and prisoner C(if he moves his head to the side of course), but prisoner B can only see prisoner C and prisoner C and D can only see the wall.
Next, the warden grabs 4 hats, two black and two white (in other variations, red and blue hates are used). Then he proceeds to show it to the prisoners and finally puts these hats on the head of each prisoner. After that, he explains the rules that prisoners can’t talk to each other and cannot twist back to see what color of hat others are wearing. Now prisoners are given a time limit to guess the color of the hat that they are wearing, different time limits are given in different variations from 10 seconds to 5 minutes. Also, no guesswork is allowed, neither they are given any second chance to guess the color, and only 1 prisoner can give the answer. Finally, the warden starts the countdown. After some time, prisoner B yells the right answer. So how did he came to this conclusion?
I know the setting of this riddle is somewhat complicated but the answer is fairly simple. The way prisoner B was able to tell the right answer is that he knew that if he and prisoner C was wearing the same colored hat, prisoner A would’ve been able to tell immediately. However, prisoner A remained silent as he didn’t know what color hat he was wearing. So logically, prisoner B thought he was wearing a different colored hat from prisoner C and they were all free to go.
As you can see the answer to this riddle wasn’t that complex, still it is one of the favorite puzzles of grandparents to engage youngsters into doing some brain activity.