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You are not logged in. #1 20120220 04:31:44
Weighings  A sack of flourA grocer has a sack of flour which weights 10 kgs, 2 weights of 200 and 300 grams and a 2pan balance. #2 20120415 02:46:32
Re: Weighings  A sack of flourOK. By the 1st weighing we can have: #3 20120415 03:33:52
Re: Weighings  A sack of flourHi anna_gg; 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. #4 20120415 04:20:15
Re: Weighings  A sack of flourhi bobbym, You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #5 20120415 04:30:15
Re: Weighings  A sack of flourLATER EDIT: I am in the process of correcting this 'solution'. I am optimistic that I'll get there some time (... length of time unspecified ...) A weight derived at 1st weighing will have subscript 1. I did have some others here, not multiples of 100. I have now removed these. I do not think something like 4850 can later generate a multiple of 100 except by restoring the number that made it. This conjecture needs proving (or a counter example). I believe this is a complete list of 1st weighings. These 1st weighing amounts are put into bags and become additional 'weights'. Now, what can be made at the 2nd weighing? Theorem: (i) Where different flour bags are used the subscript total to achieve a new weight must be strictly less than the subscript of the new weight. * (ii) but if the same bag is used in several stages the subscript total to achieve a new weight need not count this bag repeatedly to make this total strictly less than the subscript of the new weight. An example of this is shown later in achieving 1400_3 and 1600_3. This theorem needs to be modified. My thanks to anonynmstefy for pointing this out. * so here, 2 > 1 + 0 + 0 Now those 'weights' can also be bagged up to use at the next stage. 3rd weighings I cannot find a way to do 1400. But anoninmstefy did: I think that's it. If you spot any more, please let me know. Oh darn it! I've just noticed that 5000. That'll be 5000 against 5000. So the list needs some additions. ..... Tomorrow perhaps. No better still, you've seen the method, I'll leave it as an exercise for the reader. Additionally, for whatever amount, x, that can be measured out, the amount 10000  x is also available for sale which doubles the list! List so far: I'm assuming the probability is easy to get from here. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #6 20120415 07:08:45
Re: Weighings  A sack of flourHi guys 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 20120415 07:51:53
Re: Weighings  A sack of flourI am modifying both my earlier posts to correct my stupid errors. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #8 20120415 07:55:46
Re: Weighings  A sack of flourHi Bob 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 #9 20120415 08:04:46
Re: Weighings  A sack of flourhi bob Last edited by anonimnystefy (20120415 08:08:20) 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 #10 20120415 08:09:57
Re: Weighings  A sack of flourhi Stefy, You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #11 20120415 08:16:17
Re: Weighings  A sack of flourHi bobbym 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 #12 20120415 08:30:30
Re: Weighings  A sack of flourHi bob 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 #13 20120415 08:40:35
Re: Weighings  A sack of flourhi Stefy, As I find them, I add them to the list, because I'll forget if I wait until the end. I think the 1st weighings list is now complete. The 2nd and 3rd weighings need a number of additions ... frightenly many additions. I think I'll have to let my brain rest a while and come back to the list tomorrow. Do you think anyone will mind if I unhide my answer as it is a real pain to have to deal with it like that. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #14 20120415 08:44:09
Re: Weighings  A sack of flourI will here make a list of all the quantities that were not mentioned in your earlier post,that I have found: 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 #15 20120415 08:45:37
Re: Weighings  A sack of flourHow? My brain just exploded. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #16 20120415 08:48:31
Re: Weighings  A sack of flourHi bob Last edited by anonimnystefy (20120415 08:51:02) 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 #17 20120415 08:52:11
Re: Weighings  A sack of flourOK thanks.
So you were right. I shouldn't have included 4950. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #18 20120415 08:54:37
Re: Weighings  A sack of flourI am trying to figure out if 1900 can be done,but I think that 5050 and 4950 are incorrect. How do you know when you have put 5050 on the left? 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 #19 20120415 09:35:39
Re: Weighings  A sack of flourHi bob I will soon or tomorrow post more. Last edited by anonimnystefy (20120415 10:24:03) 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 #20 20120415 09:47:13
Re: Weighings  A sack of flourHere's some more: Last edited by anonimnystefy (20120415 10:24:46) 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 #21 20120415 10:21:45
Re: Weighings  A sack of flourWith those numbers we have got all of the possibilities from 100 to 4000,excluding 3900,and by taking the "complements" i.e. the flour that is left in the sack we have also all the possibilities from 6000 to 10000 except 6001. The rest I conjecture to be unobtainable within the given restaints. I will try to prove that in my next post. Last edited by anonimnystefy (20120415 10:34:15) 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 #22 20120415 10:45:14
Re: Weighings  A sack of flourThis is proof that the numbers from 4001 to 5999 are unobtainable within the given restraints: Last edited by anonimnystefy (20120415 10:48:33) 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 #23 20120415 15:12:08
Re: Weighings  A sack of flourCan anyone check if these above are correct? 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 #24 20120415 17:55:21
Re: Weighings  A sack of flourI have tidied up post #5 and 'unhidden' it. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #25 20120415 18:12:56
Re: Weighings  A sack of flourHi bob 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 