tag:blogger.com,1999:blog-1147784181901427860.post2976878003799278966..comments2017-11-28T03:44:40.705-08:00Comments on The Weekly Riddle: The Prisoners' Hats, Part 1Charlie Guthriehttp://www.blogger.com/profile/15624106792764866509noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-1147784181901427860.post-34109033979032328002017-10-27T13:57:20.590-07:002017-10-27T13:57:20.590-07:00Searches related to you are in prison with barry a...Searches related to you are in prison with barry and albert. the 3 of you are in a line looking straight ahead. you're in front, then barry, the nalbert. a guard has 3 black and 2 white hats.he randomly puts one on each of your heads. albert can see your hat and barry's. barry can see your s, and you can see no ones. none of you know what color you have on your own head. the guard says if anyone can tell me with 100% certainty the color on your own hat, uttering no one else's, you may all go free. he tells albert to go first. albert is a very honest and intelligent person, but he says i don't know theres no way of knowing for sure. the guard goes to barry. barry is also intelligent and rational, but he also cannot tell. he comes to you and you say the color of your hat with 100% certainty, the guard has no choice but to release all 3 of you<br />I got this in my work email. I just wanted to know if yall can figure it out. cause I'm super confusedAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-1147784181901427860.post-41194373070200200712017-09-23T08:48:11.613-07:002017-09-23T08:48:11.613-07:00This is a great post. I like this topic.This site ...This is a great post. I like this topic.This site has lots of advantage.I found many interesting things from this site. It helps me in many ways.Thanks for posting this again.<br /><a href="https://www.kalikardiaapparel.com/" rel="nofollow">Hats</a><br />poulous bhattihttps://www.blogger.com/profile/16361753546104244498noreply@blogger.comtag:blogger.com,1999:blog-1147784181901427860.post-31936549983568774882012-12-11T08:58:16.879-08:002012-12-11T08:58:16.879-08:00This riddle ONLY works if Carl is blind. If they a...This riddle ONLY works if Carl is blind. If they all can see and are of equal intelligence 1) someone will dash out if they see 2 blacks, so no one has 2 blacks if any hesitation; 2) someone will dash out if they see 1 black and 1 white, since they know their hat must be white; 3) but with more hesitation they all rush out knowing they all have white.<br /><br />Albert, Barry, and Carl with 1 = white and 0 = black:<br /><br />A B C<br />1 1 1<br />0 1 1<br />1 0 1<br />1 1 0<br />0 0 1<br />1 0 0<br />0 1 0<br /><br />If Carl is blind, then Albert and Barry could make no inferences based on Carl's actions. C knows he and B aren't both in black since A didn't run out, and he and A aren't both in black since B didn't run out. So the only possibilities now are:<br /><br />A B C<br />1 1 1<br />0 1 1<br />1 0 1<br />1 1 0<br />0 0 1<br /><br />Blind Carl knows Albert and Barry would be racing out if Carl had black, because they've made all the same intelligent inferences. So, Carl knows he has white before the others know, if everyone is standing around hesitating.Trevor Sayrehttps://www.blogger.com/profile/11825445816648130429noreply@blogger.comtag:blogger.com,1999:blog-1147784181901427860.post-74038111119688161382012-11-14T06:41:03.076-08:002012-11-14T06:41:03.076-08:00What if Carl wears a black hat, and the other two ...What if Carl wears a black hat, and the other two white hats? They both see that there are one of each color and nobody can be sure which is on their head. Maybe if Carl wasn't blind this riddle would workAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-1147784181901427860.post-42477905573066666702012-10-27T23:58:55.042-07:002012-10-27T23:58:55.042-07:00The silence of the other prisoners says a lot - bu...The silence of the other prisoners says a lot - but there are some assumptions here that are being forgotten. I think this page does a good job of clarifying assumptions:<br /><br /><br />http://www.programmerinterview.com/index.php/puzzles/hat-puzzle-black-and-white-hats/Joehttps://www.blogger.com/profile/12568980537278420520noreply@blogger.comtag:blogger.com,1999:blog-1147784181901427860.post-54618866369952317922009-12-13T21:16:30.769-08:002009-12-13T21:16:30.769-08:00Since the solution hasn't been posted, I figur...Since the solution hasn't been posted, I figured I'd go ahead and put in a brief explanation. Fun puzzle, by the way.<br /><br />Carl's hat is white, and he can infer this from Albert and Barry's inability to tell the colors of their own hats.<br /><br />Given that there are only two black hats available, there are seven possible arrangements of hats among the three prisoners:<br /><br />(the table won't go in, because preformatted text is not allowed. Unfortunate. If you like, you can make a table with seven rows and three columns. Let a white hat encode binary zero, and a black hat encode binary one. Then, if Albert's hat color is the MSB, Barry's is in the middle, and Carl's is the LSB, row n is given by the binary representation of n-1.)<br /><br />An eighth scenario, in which each of the prisoners wears a black hat, is impossible, since there are only two black hats.<br /><br />Consider what Albert can infer from seeing Barry's and Carl's hats. The only way he could make a conclusive determination of his own hat color is if Barry and Carl were both wearing black hats. In that case, Albert would know he was wearing white. Since Albert is honest and intelligent, and does not know that he is wearing white, we know that Barry and Carl are not both wearing black hats -- this eliminates line 4 from the table above.<br /><br />Likewise, if Albert and Carl were both wearing black hats, Barry would immediately know that his hat was white. Since he doesn't know this, we can eliminate line 6.<br /><br />Finally, Barry knows that he and Carl are not both wearing black hats. If they were, Albert would know that his own hat was white. So, if Carl were wearing a black hat, and Albert's hat were white, Barry would know that his own hat must be white. Since he cannot infer this, Carl knows that his hat is white.Zachhttps://www.blogger.com/profile/11107439993314759422noreply@blogger.com