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You are not logged in. #1 20120820 16:51:58
21 Marbles in 3 hatsFind the solution for the following: There are 3 hats with 11, 6, and 4 marbles, respectively. On a single move we can remove one marble from one of the hats, one marble from some other hat, and place both removed marbles to the third hat. Can we reach a situation where there are 7 marbles in each hat after some number of moves? If so, show the way. If not, provide some argument why not? #2 20120820 19:18:30
Re: 21 Marbles in 3 hatsHi mbop; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20120820 23:18:25
Re: 21 Marbles in 3 hats
#4 20120820 23:27:19
Re: 21 Marbles in 3 hatsI think itis impossible to get all three to be 7. I'm working on a proof. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #5 20120820 23:27:58
Re: 21 Marbles in 3 hatsWhat would be the next nos. in the no. series 1,2,12,12,30,.?.,.?., #6 20120820 23:30:07
Re: 21 Marbles in 3 hatsHi Phoolwati The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #7 20120821 03:26:26
Re: 21 Marbles in 3 hatsHi mbop, Code:7,7,7 8,8,5 9, 9,3 9,6,6 10,10,1 10,7,4 11,8,2 11,5,5 12, 9,0 12,6,3           8,8,5 9,9,3 10,10,1 10,7,4 11, 8,2 11,8,2 12,9,0 12,6,3 13, 7,1 13,7,1 9,6,6 10, 7,4 7,7,7 11,5,5 12,6,3 9,6,6 10,10,1 13,4,4 8,8,5 9,9,3 10,7,4 ====================================================================================== 13,7,1 13,4,4 14,5,2 15,6,0 15,3,3 16,4,1 17,2,2 18,3,0 19,1,1          14,5,2 14,5,2 15,6,0 16,4,1 16,4,1 17,2,2 18,3,0 19,1,1 17,2,2 11,8,2 11,5,5 15,3,3 13,7,1 13,4,4 14,5,2 15,3,3 16,4,1 12,6,3 Last edited by phrontister (20120821 23:07:56) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #8 20120821 05:49:41
Re: 21 Marbles in 3 hatsHi phontister and anonimnystefy; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #9 20120822 17:02:37
Re: 21 Marbles in 3 hatshi Phoolwati Did I bother to work this out? Must be losing my marbles. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #10 20120823 00:46:18
Re: 21 Marbles in 3 hatsHi, Last edited by phrontister (20120823 19:02:06) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #11 20120823 01:45:59
Re: 21 Marbles in 3 hatsHi phrontister; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #12 20120823 05:51:54
Re: 21 Marbles in 3 hatsHi Bobby, "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #13 20120823 06:25:07
Re: 21 Marbles in 3 hatsHi phrontister; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #14 20120823 09:50:23
Re: 21 Marbles in 3 hatsHi Bobby, Last edited by phrontister (20120823 09:52:36) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #15 20120824 01:59:05
Re: 21 Marbles in 3 hatsEDIT: Ignore this post (replaced by post #19 & #20). The two different subscripts denote the two different groups. Examples: 11,7,3 can never reach 6,7,8 because 13,6,2 can reach 8,7,6 because Here's a sequence of moves (there are several other options too) to show how that one can be done: 13,6,2 > 12,5,4 > 11,4,6 > 10,6,5 > 9,5,7 > 8,7,6. As for the OP's question, 11,6,4 can never reach 7,7,7 because The order of the two groups in the formula is irrelevant for this exercise. Last edited by phrontister (20120827 23:07:29) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #16 20120824 16:17:51
Re: 21 Marbles in 3 hatsHi phrontister; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #17 20120824 19:13:26
Re: 21 Marbles in 3 hatsEDIT: Ignore this post (replaced by post #19 & #20). whereas the result of the mod is 0...which, according to my formula, is why your moves worked out. I've corrected my post #15. And I think you'll find that 11,7,3 can't reach 6,7,8...according to my formula result, anyway: Last edited by phrontister (20120827 23:07:48) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #18 20120824 20:32:33
Re: 21 Marbles in 3 hatsHi phrontister; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #19 20120826 22:47:54
Re: 21 Marbles in 3 hatsHi Bobby, Last edited by phrontister (20120827 22:52:08) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #20 20120826 22:48:54
Re: 21 Marbles in 3 hatsOk. Here's my proof. I hope I can get the idea across. When applying that formula to different groups of hat contents, the results, which are either "0", "1" or "2", must be identical for those groups to be in the same stream. Any groups that satisfy that condition can reach each other after some number of moves. Applying this formula to the two puzzle groups yields the following different results: "0" for 7,7,7 and "1" for 11,6,4...which means that 11,6,4 can't reach 7,7,7 as the formula results aren't identical. Hope that makes sense! Last edited by phrontister (20120828 09:36:09) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #21 20120827 05:08:54
Re: 21 Marbles in 3 hatsHi phrontister; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #22 20120827 21:42:21
Re: 21 Marbles in 3 hatsThanks, Bobby! "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #23 20120827 21:56:03
Re: 21 Marbles in 3 hatsHi phrontister; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 