Genady Posted May 13, 2023 Share Posted May 13, 2023 There are 5 bags full of coins which look identical, but all the coins in some bags are real while all the coins in other bags are fake. Real coin weighs 10 g, fake coin weighs 9 g. Using a weighing scale, identify the bags with real and the bags with fake coins by weighing only once. PS. It is also possible that coins in all the bags are real, and that coins in all the bags are fake. Link to comment Share on other sites More sharing options...
ALine Posted May 13, 2023 Share Posted May 13, 2023 now when you say "all the coins in some bags are real and all the coins in other bags are fake." Do you mean that their are no empty bags and there are also no bags which are heterogeneous. Or that they have real and fake coins? Link to comment Share on other sites More sharing options...
Genady Posted May 13, 2023 Author Share Posted May 13, 2023 6 minutes ago, ALine said: now when you say "all the coins in some bags are real and all the coins in other bags are fake." Do you mean that their are no empty bags and there are also no bags which are heterogeneous. Or that they have real and fake coins? Correct. No empty bags. No mixed bags. All coins in each bag are either real or fake. Link to comment Share on other sites More sharing options...
ALine Posted May 13, 2023 Share Posted May 13, 2023 I was about to finish, but then I saw this trickster. 2 hours ago, Genady said: by weighing only once. Now do you mean weighing every bag all together once or can I weigh each bag independently once. Link to comment Share on other sites More sharing options...
Genady Posted May 13, 2023 Author Share Posted May 13, 2023 (edited) 18 minutes ago, ALine said: I was about to finish, but then I saw this trickster. Now do you mean weighing every bag all together once or can I weigh each bag independently once. I mean performing one measurement only. IOW, you are allowed to use the weighing scale only once. BTW, we don't know anything about the numbers of coins in the bags. These numbers may be different. We only know that there are enough coins in each bag to solve the problem. This means that weighing bags doesn't help. We need to weigh coins. You are allowed to take coins out of the bags for the weighing. Edited May 13, 2023 by Genady Link to comment Share on other sites More sharing options...
ALine Posted May 13, 2023 Share Posted May 13, 2023 hmmm, what type of weighing scale? Link to comment Share on other sites More sharing options...
Genady Posted May 13, 2023 Author Share Posted May 13, 2023 Just now, ALine said: hmmm, what type of weighing scale? Like in the picture in OP. Link to comment Share on other sites More sharing options...
ALine Posted May 13, 2023 Share Posted May 13, 2023 dang, thought it was a double scale. this is indeed a puzzle Does there have to be real and fake coins? Like their have to be bags which are real and fake? Can you have all 5 bags be fake and none real? Link to comment Share on other sites More sharing options...
Genady Posted May 13, 2023 Author Share Posted May 13, 2023 23 minutes ago, ALine said: Can you have all 5 bags be fake and none real? Yes. As I said in the OP, Quote PS. It is also possible that coins in all the bags are real, and that coins in all the bags are fake. Link to comment Share on other sites More sharing options...
CharonY Posted May 14, 2023 Share Posted May 14, 2023 Can I take coins out of the bags? Link to comment Share on other sites More sharing options...
TheVat Posted May 14, 2023 Share Posted May 14, 2023 (edited) Yes. Spoiler Label bags, one thru five. Take one coin from bag one, two from bag 2, and so on. If one is fake, then the maximum possible weight (150) drops by one. If two is fake, then drops by 2. You get basic idea. Edited May 14, 2023 by TheVat tmi Link to comment Share on other sites More sharing options...
Genady Posted May 14, 2023 Author Share Posted May 14, 2023 (edited) 27 minutes ago, CharonY said: Can I take coins out of the bags? Yes. (You have to.) 19 minutes ago, TheVat said: Yes. Hide contents Label bags, one thru five. Take one coin from bag one, two from bag 2, and so on. If one is fake, then the maximum possible weight (150) drops by one. If two is fake, then drops by 2. You get basic idea. Spoiler Almost there, but I need to know what is "so on." How many each from the other three bags? Spoiler How do you get max 150? Ah, I see: 1+2+3+4+5? This will not work, sorry. Edited May 14, 2023 by Genady Link to comment Share on other sites More sharing options...
TheVat Posted May 14, 2023 Share Posted May 14, 2023 (edited) Spoiler We were leaving the house, last night, so I had to stop in the middle of problem. Yes, I realize the number series (coins in each pile) must be such that no sum of any group of the numbers is the same, because that would give ambiguous answer. I think powers of two would work? 1,2,4,8,16 Edited May 14, 2023 by TheVat hide function woe 1 Link to comment Share on other sites More sharing options...
Genady Posted May 14, 2023 Author Share Posted May 14, 2023 13 minutes ago, TheVat said: Reveal hidden contents We were leaving the house, last night, so I had to stop in the middle of problem. Yes, I realize the number series (coins in each pile) must be such that no sum of any group of the numbers is the same, because that would give ambiguous answer. I think powers of two would work? 1,2,4,8,16 Spoiler Yes. Any base would work, but base 2 is the most efficient, i.e., answers the question with the smallest number of coins weighed. Just convert the missing grams to a binary number. E.g., 17 is 10001 in the binary system, which says that the bags #1 and #5 contain fake coins. Link to comment Share on other sites More sharing options...
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