logic Question: five hats and three geniuses

L

LadyC

New member
Joined
Apr 9, 2008
Messages
2
I need help with ths logic question. Please give me step by step help

Three geniuses stand in a file (one behind the other). Each can see only to the front, so the rear person can see the middle and the front, the middle person can see the front, and the genius in the front cannot see anyone.

You have five hats. Two are white, and three are red. You blindfold the three geniuses, who are utterly truthful, and put a hat – at random – on the head of each. Then you hide the other two hats and remove the blindfolds.

You then ask each genius to name the color of his hat (which he cannot see).

The rear one says "I don't know." The middle on says, "I don't know." Then the front one says, "I know."

WHAT COLOR IS THE FRONT GENIUS' HAT??????
 
What are your thoughts? What have you tried? How far did you get? What conclusions have you drawn?

Please be complete. Thank you! :D

Eliz.
 
To get you started:
if the rear guy sees 2 whites, he'd know he has a red;
that's the way you must "think this out";
if you can't continue, sorry: we can't think for you!
 
Denis said:
To get you started:
if the rear guy sees 2 whites, he'd know he has a red;
that's the way you must "think this out";
if you can't continue, sorry: we can't think for you!
Click to expand...

Thank you for your help.
 
I need help with ths logic question. Please give me step by step help
Three geniuses stand in a file (one behind the other). Each can see only to the front, so the rear person can see the middle and the front, the middle person can see the front, and the genius in the front cannot see anyone.
You have five hats. Two are white, and three are red. You blindfold the three geniuses, who are utterly truthful, and put a hat – at random – on the head of each. Then you hide the other two hats and remove the blindfolds.
You then ask each genius to name the color of his hat (which he cannot see).
The rear one says "I don't know." The middle on says, "I don't know." Then the front one says, "I know."
WHAT COLOR IS THE FRONT GENIUS' HAT??????

DENIS gave you a great clue. Assuming that each person was equally smart, they each realized that there were only 7 possible ways of adorning their heads with the 3 red and 2 white hats. They were:

Cand. #.....................1 2 3
........................... R R R
............................R R W
............................R W R
............................W R R
........................... W W R
............................W R W
............................R W W

As stated, #1, opts not to answer as he cannot tell what his hat color is. Why not? Well, if he had seen 2 white hats on #2 and #3, he would have immediately known that his hat had to be red. Since he does not answer, he must be seeing either 2 red hats or 1 red and 1 white hat, eliminating combination #7 and thus having no way of determining the color of his hat.

#2 being just as smart as #1, realizes that since #1 did not answer, #1 must be seeing either 2 red hats or 1 white hat and 1 red hat. Therefore, ???

Keep in mind that all three are genius' and each can draw the ssme conclusions as each of the persons behind them.

Have you had any further success. Please let us know.
 
You must log in or register to reply here.
Top