Forum Mind Puzzles - 3

[Sikslik7]

With no one solving the still unsolved second puzzle http://www.343industries.org/forum/topic/27425-forum-mind-puzzles-2/ I am forced to continue on without a correct solution.

 

 

The third puzzle involves reasoning, and comprehension of cause and effect.

 

There is a story of three Russian professors who were going to be executed for spreading Democratic ideas in Soviet Russia during the 30's. Stalin decided to make an example of them, by giving the professors a chance to walk free - a fair Democratic chance in a dictator run Communist country. Unknown if this actually occured, but widely believed to be from 50's Red Scare propaganda.

 

The puzzle:

 

Stalin has the professors lined up before him in a large room. Before him are five identical hats, except for their respective colors. Three are black, and two are white. The professors are blindfolded, and turned 90 degrees to the right. One hat is put on top of each of the men, and the remaining hats are put into a opaque bag. The professors' blindfolds are taken off. There are no mirrors or reflective objects in the room, and there are only the five hats (three on the professors and 2 in the bag.

 

Stalin tells them that if any one of them correctly states the color of the hat on top of his own head (the man answering that is), all three of them are free to go, but if they answer incorrectly, the three men would die. The men were not allowed to talk or move or make any gestures except for when answering. No one was allowed talk to them or communicate in any way, and the room contains no hints.

 

After a few minutes pass, the third professor correctly states the color of his hat, "my hat is black", but he did not guess. How did he know the color of his hat? (please give a lengthy response, with all reasoning explained)

 

Also:

The professors are arranged as such (> means the professor is looking in that direction):

 

1> 2> 3>

 

 

 

Good luck!

 

 

Solution found by JI1223 X on 4/8/13. Nice job!

Edited April 8, 2013 by Sikslik7

[BaconShelf]

The hats were lined up like this. ( means black

(W) means white

 

B B B W W

 

1 2 3

 

 

The three professors were In front of the three black hats?

 

Stupid smileys.

B means black

[Surveillance]

WHY DOES IT HAVE TO BE RUSSIANS?!?!?!??!

[Is not JL]

Got it.

 

All 3 are professors, after all. They know each other are clever. So the 3rd could get it - He thought it like this.

 

I'll generally refer to the professors as 1st, 2nd and 3rd. 

 

The 1st professor can see both the had of 3rd and 2nd. If 1st sees 2 white hats, he would've immediately answered - its 100% he's wearing black. But no, he didn't answer! This means: 2nd and 3rd are either wearing 2 black hats, or one are wearing black and one are wearing white. Those are the only combinations possible.

 

Now the 2nd knows this, and he can see 3rd. So he thinks, maybe I have black. Maybe I have white. I don't know. So he will look forward and see if its black or white. If it's white, then he can answer as black because of why first didn't answer - he would have a black hat. But no, he sees 3rd has a black hat, and so he doesn't know if he has a black hat or a white hat.

 

Now, 3rd knows both of this - he has run this logic in his mind. And, since 2nd didn't answer, he therefore reaches the conclusion that he has a black hat.

 

Answered.