5125kaf@hound.UUCP (K.FRIEDMAN) (02/09/86)
Three men are in a room. The room has no mirrors and the three men
are in a straight line such that the person in the back of the line
can see the two people in front of him, the middle person can see
only the person in front of him, and the person in front can't see
anyone. Another person walks in with a bag containing 3 black hats
and two red hats. The man pulls three hats at random out of the bag
and places them randomly on the three men. He walks out of the room.
The man in the back says,"I don't know what color hat I'm wearing."
The man in the middle says,"I don't know what color hat I'm wearing, either."
Now tell me what color hat the man in the front of the line is wearing
and why.
*** GOOD LUCK ***
Barry Friedman
ihnp4!houxm!hound!5125kafchip@mtuni.UUCP (Charles Maurer) (02/11/86)
> > > Three men are in a room. The room has no mirrors and the three men > are in a straight line such that the person in the back of the line > can see the two people in front of him, the middle person can see > only the person in front of him, and the person in front can't see > anyone. Another person walks in with a bag containing 3 black hats > and two red hats. The man pulls three hats at random out of the bag > and places them randomly on the three men. He walks out of the room. > The man in the back says,"I don't know what color hat I'm wearing." For the man in back to know for sure what color hat he was wearing, the two men in front of him would both have to be wearing red hats. This would mean he would have a black hat on his own head. Since he can't determine his hat color, at least 1 of the men, if not both, in front of him must have a black hat. > The man in the middle says,"I don't know what color hat I'm wearing, either." The man in front of him, upon hearing the response from the man behind him would realize that either himself or the man in front of him HAS to be wearing a black hat, with the other hat being red or black. If the man in front was wearing a red hat, then the middle man would know for sure that he was wearing a black hat. If the man in front was wearing a black hat, then the middle man could be wearing either a black or a red hat, so the man in front must be wearing a black hat. > Now tell me what color hat the man in the front of the line is wearing > and why. > > > *** GOOD LUCK *** > > > Barry Friedman > ihnp4!houxm!hound!5125kaf
latham@bsdpkh.UUCP (Ken Latham) (02/12/86)
> > > Three men are in a room. The room has no mirrors and the three men > are in a straight line such that the person in the back of the line > can see the two people in front of him, the middle person can see > only the person in front of him, and the person in front can't see > anyone. Another person walks in with a bag containing 3 black hats > and two red hats. The man pulls three hats at random out of the bag > and places them randomly on the three men. He walks out of the room. > The man in the back says,"I don't know what color hat I'm wearing." > The man in the middle says,"I don't know what color hat I'm wearing, either." > Now tell me what color hat the man in the front of the line is wearing > and why. > > > *** GOOD LUCK *** -------------- NOT "GOOD LUCK" ------------ GOOD LOGIC -------------------- if the 3rd man (man in back) doesn't know then the two in front of him are not both wearing red hats ( else he would know his to be black ) therefore #1 and #2 must be either both black or a red and a black #2 having figured this out as any intelligent person could (assumed) would know his hat color if #1 were wearing a red hat. therefore the man in front (#1) is wearing a black hat! _______________________________________________________________________________ | | | | Ken Latham | uucp: ihnp4!bsdpkh!latham | | AT&T-IS | uucp: {ihnp4!decvax,peora}!ucf-cs!latham | | Orlando , FL | arpa: latham.ucf-cs@csnet-relay | | USA | csnet:latham@ucf | |_____________________________|_______________________________________________| -- Concerning those who have a great deal of experience: " There are those who have many experiences... and those who have one experience many times." _______________________________________________________________________________ | | | | Ken Latham | uucp: ihnp4!bsdpkh!latham | | AT&T-IS | uucp: {ihnp4!decvax,peora}!ucf-cs!latham | | Orlando , FL | arpa: latham.ucf-cs@csnet-relay | | USA | csnet:latham@ucf | |_____________________________|_______________________________________________|
ice@trwrba.UUCP (Douglas L. Ice) (02/12/86)
Summary:Red&Black hats (NON-ROT SPOILER!!!) Expires: References: <1645@hound.UUCP> Sender: Reply-To: ice@trwrba.UUCP (Douglas L. Ice) Followup-To: Distribution: Organization: TRW EDS, Redondo Beach, CA Keywords: In article <1645@hound.UUCP> 5125kaf@hound.UUCP (K.FRIEDMAN) writes: > > > Three men are in a room. The room has no mirrors and the three men >are in a straight line such that the person in the back of the line >can see the two people in front of him, the middle person can see >only the person in front of him, and the person in front can't see >anyone. Another person walks in with a bag containing 3 black hats >and two red hats. The man pulls three hats at random out of the bag >and places them randomly on the three men. He walks out of the room. >The man in the back says,"I don't know what color hat I'm wearing." >The man in the middle says,"I don't know what color hat I'm wearing, either." >Now tell me what color hat the man in the front of the line is wearing >and why. > I believe we must assume that the man in the back and the middle man both know that there were 3 black hats and 2 red hats in the bag (or at least that there were only 2 red hats available). If the front and middle men both wore red hats, then the back man would know that he wore a black hat. But he doesn't know, so either the front or middle man wears a black hat. Now if the middle man, knowing this, sees a red hat on the front man, he would know that he wears a black hat. Since he doesn't know this, the front man must wear a black hat. (Sorry about the verb tense changes) --------------------------------------------------------------------- --- Doug Ice
verma@ucla-cs.UUCP (02/13/86)
In article <1645@hound.UUCP> 5125kaf@hound.UUCP (K.FRIEDMAN) writes: > > > Three men are in a room. The room has no mirrors and the three men >are in a straight line such that the person in the back of the line >can see the two people in front of him, the middle person can see >only the person in front of him, and the person in front can't see >anyone. Another person walks in with a bag containing 3 black hats >and two red hats. The man pulls three hats at random out of the bag >and places them randomly on the three men. He walks out of the room. >The man in the back says,"I don't know what color hat I'm wearing." >The man in the middle says,"I don't know what color hat I'm wearing, either." >Now tell me what color hat the man in the front of the line is wearing >and why. The man in front is wearing a black hat. Why --- Since the man in the back did not know what color his own hat was, then at least one of the men in front of him was wearing a black hat. For if both of the men in front of him were wearing red hats, then he would know his own hat was black (only 2 red hats). Now the middle man still does not know his own hat's color; if the first man had been wearing a red hat, then the man in the middle (knowing one of the two had a black hat) would know he was the one. But he didn't so the first man was not wearing a red hat, and therefore must have been wearing a black hat. QED TS Verma
ken@osiris.UUCP (Ken Harkness) (02/13/86)
> > > Three men are in a room. The room has no mirrors and the three men > are in a straight line such that the person in the back of the line > can see the two people in front of him, the middle person can see > only the person in front of him, and the person in front can't see > anyone. Another person walks in with a bag containing 3 black hats > and two red hats. The man pulls three hats at random out of the bag > and places them randomly on the three men. He walks out of the room. > The man in the back says,"I don't know what color hat I'm wearing." > The man in the middle says,"I don't know what color hat I'm wearing, either." > Now tell me what color hat the man in the front of the line is wearing > and why. > > > Barry Friedman > ihnp4!houxm!hound!5125kaf Black. If #1 and #2 had red hats on, #3 would know that he had a black one, so either #1 and #2 have both black hats or one they have 1 of each color. However, if #1's hat is red, then #2 knows he must have a black hat on, since he knows that it cannot be red (from sentence 1). Therefore, #1's hat is black. ken harkness seismo!umcp-cs!aplcen!osiris!ken
terryl@tekcrl.UUCP (02/14/86)
> > > Three men are in a room. The room has no mirrors and the three men > are in a straight line such that the person in the back of the line > can see the two people in front of him, the middle person can see > only the person in front of him, and the person in front can't see > anyone. Another person walks in with a bag containing 3 black hats > and two red hats. The man pulls three hats at random out of the bag > and places them randomly on the three men. He walks out of the room. > The man in the back says,"I don't know what color hat I'm wearing." > The man in the middle says,"I don't know what color hat I'm wearing, either." > Now tell me what color hat the man in the front of the line is wearing > and why. > The first man is wearing a black hat. At first, this looked impossible to figure out, but once you look at it logically, you'll say "WOW!!! I coulda had a V8!!!". Here's the reasoning: From the vantage point of the men in the back of the line, there are three possibilities: The two men in front both have black hats, or both have red hats, or one has a red hat and one has a black hat. We can immediately dismiss the "both have red hats" case, since if that were true, then the man in the back of the line would have a black hat. That leaves either "both have black hats" case, or "one has a red hat and the other has a black hat" case. We only need to consider the "one has a red hat and the other has a black hat" case, since if both the man in front and the man in the middle had a black hat, then obviously the man in front would be wearing a black hat. Assume the man in front had a red hat. Now the man in the middle AND the man in the back can both see this. If this were the case, then the man in the middle can immediately claim that he is wearing a black hat, because by what the man in the back said. So the man in front cannot be wearing a red hat, because the man in the middle claims that he doesn't know what color hat he is wearing; therefore, the man in front must be wearing a black hat. QED. Terry Laskodi of Tektronix