| Author |
 Topic  |
|
|
westworld
Average Member
USA
19 Posts |
 Posted - 04/09/2012 : 23:03:23
|
Alice stands facing a wall, Bob stands behind Alice, Carol is behind Bob, Dave is behind Carol, and Eve is behind Dave. All five are facing the wall.
The five are blindfolded and three white hats and two black hats are placed on their heads. When the blindfolds are removed each person can see all the hats in front, but not his or her own hat or any of the hats behind.
Dave says, "I do not know what color my hat is." Bob replies, "Neither do I." Then Alice says, "I know what color my hat is."
What color is Alice's hat?
|
 |
|
|
the_hill1962
Advanced Member
USA
1440 Posts |
Posted - 04/10/2012 : 12:35:36
|
You seem to post puzzle type of problems all the time with no statement of what you have tried to do in order to solve them. All you do is post the problem.
So, are these problems from a class that you are taking or are you just doing these problems for fun?
For this problem, just like most of your other problems that you have posted, do the elimination process.
All you have are two things to try:
1. Alice's hat is white
2. Alice's hat is black
If her hat is white, then when Dave says he doesn't know his, that means both Bob and Carol can't each have a white cap also because then Dave would know his is black (since there are just 3 white caps and he would be seeing all 3). You would then test the situations for Bob having black and Carol white or visa versa. You know they aren't both black because Dave would have know his is white (since there are just 2 black hats).
If her hat is black, then when Dave says he doesn't know his, that means Bob and Carol are BOTH white (since if either was black, he would be seeing two black hats and then know his is white).
Once you go through the details of the above, you will either be able to eliminate one of the choices. If you find that #1 (Alice white) doesn't work for one of the 'situations', then her hat is black.
If you find that #2 (Alice black) doesn't work, then her hat is white.
Of course, this could be a trick problem and the answer could be "not enough information". |
|
|
| |
Topic |
|
|
|
Interactive Math Goodies Software
at tricck
