tag:blogger.com,1999:blog-3722233.post3414701886510230603..comments2021-12-06T22:20:37.890-06:00Comments on Computational Complexity: 89944 Hat ProblemsLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-3722233.post-81012856769416438712017-07-19T10:16:30.856-05:002017-07-19T10:16:30.856-05:00AH- you bring up an interesting point.
One of the...AH- you bring up an interesting point.<br /><br />One of the solutions of Winklers Problem (with randomly assigned hats, maximizing the expected number of people who get it right) does indeed USE Hamming codes.<br /><br />Hence a real world thing (Hamming codes) is applied to get a solution to a Hat puzzle.<br /><br />I thing you are looking for a hat puzzle solution be used for a real world problem.<br /><br />Alas, if Hat puzzles came first then math developed for Hat Puzzles would THEN be used for a real world application.<br /><br />This is almost a cliche: mathematics developed for real applied reasons without thinking of some pure math application, later used for pure math. We need to Fund and study more applied math to help us with our pure math problems!GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-17104807044128877552017-07-18T19:11:32.006-05:002017-07-18T19:11:32.006-05:00Hamming Codes?
Hamming Codes?<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-25988247676934628482017-07-18T10:34:54.570-05:002017-07-18T10:34:54.570-05:00Good question.
But actually I've never seen a ...Good question.<br />But actually I've never seen a hat problem that even claimed some application--- I invite my readers to leave comments about<br /><br />a) Has any paper even claimed an application (and not to some other branch of math)?<br /><br />b) Has any paper or result really been applied?<br /><br />I'm skeptical, but I've been skeptical before and found out something had an application!<br />GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-36247578934552311152017-07-18T06:56:19.792-05:002017-07-18T06:56:19.792-05:00Thanks Bill for sharing. can u please tell us whic...Thanks Bill for sharing. can u please tell us which of these toy problems has real time applications or is used in some way in industry or theory ... be it either crypto or some other field. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-30430885959259769172017-07-18T01:31:53.835-05:002017-07-18T01:31:53.835-05:00I remember reading my first hat problems in Raymon...I remember reading my first hat problems in Raymond Smullyan's books as a child, but he told them with colored stamps on the forehead of the players (so that each could see the others' stamps but not his).<br /><br />In one of these puzzles, two stamps were put on each player's head (you can also to that with hats, but you'd have to stack two hats). I couldn't find the exact problem on the net, but it was something along the lines of :<br />3 perfect logicians A, B and C are shown 4 red stamps and 4 blue stamps. Two of these stamps are put on the head of each logician and the remaining two are hidden away. Each can see the stamps on the others' heads but not his.<br />They are asked one after the other if they can deduce the colors of their stamps. A, B, C all say they can't. Then A is asked again and he still says no. Finally B is asked again and says he knows the color of his stamps.<br />What are the colors of B's stamps ?<br /><br />I might have gotten it wrong, and should think about it more thoroughly to make sure this presentation is the right one, but the point here is that some hat problems variations put more than one hat on players' heads (and it cannot simply be converted into a problem with one hat and n * n colors).Zanaphernoreply@blogger.com