The Hat Contest
Four men stand in a line, one behind the other, all facing the same direction, like so:
[#1].....[#2].....[#3].....[WALL].....[#4]
There is a wall between #s 3 and 4, so #s 1, 2, & 3 cannot see #4.
#1 can see #s 2 & 3, and #2 can see #3. #s 3 and 4 cannot see anyone else.
The men are all wearing hats. Two of the hats are white and two are black, but the men don't know what color hats they are wearing. However by looking at and listening to one another, they can figure it out. As they do, they will shout out the color of the hat they are wearing.
The first person to shout out his correct hat color will win $100, the second will win $50, and the third will win $25. Shouting out the wrong color will disqualify the person, as will turning around or taking off one's hat or talking to one another.
How much will each person win?
* Posted by Sammy's Dad. If you figure out the right answer, don't tell Sammy.
[#1].....[#2].....[#3].....[WALL].....[#4]
There is a wall between #s 3 and 4, so #s 1, 2, & 3 cannot see #4.
#1 can see #s 2 & 3, and #2 can see #3. #s 3 and 4 cannot see anyone else.
The men are all wearing hats. Two of the hats are white and two are black, but the men don't know what color hats they are wearing. However by looking at and listening to one another, they can figure it out. As they do, they will shout out the color of the hat they are wearing.
The first person to shout out his correct hat color will win $100, the second will win $50, and the third will win $25. Shouting out the wrong color will disqualify the person, as will turning around or taking off one's hat or talking to one another.
How much will each person win?
* Posted by Sammy's Dad. If you figure out the right answer, don't tell Sammy.
Labels: SharedPuzzle
posted by Rajesh Lal at
11:53 AM
12 Comments:
If #s 2 and 3 are both wearing one colour hat, then #1 will know that he is wearing the other colour hat, and so can say and win $100. #2 will see which colour #3 has, and would know that he must have the same colour hat as #3, as that is the only way #1 could have known for certain, so he will win $50. #3 would then be able to realise that for the other two to know, he must have the same as #2 as that is the only way he could have known, so he will win $25. This leaves #4 to say the remaining colour, and win nothing.
Of course, if #1 is guessing, or #s 2 and 3 are wearing different colour hats then this does not apply.
I think adstaaa is right as far as he/she goes, however #4 could also realise that if #1 and #2 both call the same colour then he must have the other, then 3rd prize goes to whoever of #3 and #4 reacts to this the quickest.
If #2 and #3 have different colours then when #2 hears nothing from #1 he will will know that his colour is different to #3 and call accordingly. #3, on hearing from #2 first will call the opposite to #2 to claim 2nd prize. #1 and #4 will both remain in the dark and be unable to call for sure. However a guess by either gives that man a 50% chance of third prize one of them will be the first to have a go.
Chris
This is a bit of a weak riddle, since there are multiple possibilities for answers, depending on how smart the different men are, and whom is wearing what color hat. A good riddle has only one answer, that requires third level logic to arrive at.
I came up with both of the above answers, but slightly different than ADSTAAA's version.
If #1 sees #2 and #3 are the same, then he should immediatly know his is oppisite and call it out. Upon hearing #1.. all the rest should immediatly know there's.. they'll all know that #2 and # are the same. So #2 and #3 shout out the oppisite of what #1 and #4 shouts the same...it just depends on how quick they are to shout out their colors.
Anon is right on the other scenario.. if #1 hesitates, then #2 and #3 must be oppisite, so #2 will answer 1st and #3 after him.. #1 and #4 can't know for sure..
So, can #2 or 3 ask #1 what hat they are wearing? cause that might put a whole new dynamic on this situation...
each one will get 0 dollars. They can't figure it out, because they can't talk, turn around, or take off teir own hat. since no one can see te 4th man's hat, they can't posibly figure it out without being disqualified.
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the question is "how much would each person win?"
so the answer is:
$100, $50 or $25!
simple as that!
there is no way you will know who will win because the question is incomplete. Like what color each person has.
if this is the case
1White 2White 3Black 4Black
then number 1 will win
if its like this:
1White 2Black 3White 4Black
all of them have 50/50 chance..
oopps I got that wrong..
1white 2black 3black 4white
or
1black 2white 3white 4black
is the only combination (both 2 and 3 are the same)that will have a clear winner
$100, $50, $25
its a trick
#2 = $100
#1 = $50
#3 = $25
-EscaLayer™
if #1 can see #2 &3 wearing black and white hats or vice versa, then #2 will win, next is #3, but for the third prize no one wins. If #1 sees two black hats or two white hats, then he wins for sure, but the next prizes depends on how fast#2  say the color of their hats.
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