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Posers and Puzzles

Posers and Puzzles

  1. 27 Jan '05 10:46 / 1 edit
    You have 10 sacs of coins. All the sacs contain coins that weigh the same = 10 grams. One sac of coins is odd and contains coins that weigh 9 grams. How to find out which sac contains the odd coins with only one try?
    You have 10 sacs of coins. All the sacs contain coins that weigh the same = 10 grams. One sac of coins is odd and contains coins that weigh 9 grams. How to find out which sac contains the odd coins?
  2. Standard member TheMaster37
    Kupikupopo!
    27 Jan '05 10:56
    My guess is that you'll need at least 3 weighings to determine.

    Of course you might hope you're lucky and simply weigh two sacs at random.
  3. Standard member Palynka
    Upward Spiral
    27 Jan '05 13:04
    Originally posted by yevgenip
    You have 10 sacs of coins. All the sacs contain coins that weigh the same = 10 grams. One sac of coins is odd and contains coins that weigh 9 grams. How to find out which sac contains the odd coins?
    put 1 coin from the first sac, 2 from the second,..., 10 from the tenth.

    if all coins weighed the same this selection should weigh 55.

    If it weighs 54 it's the first, 53 it's the second...45 is the tenth.
  4. Standard member TheMaster37
    Kupikupopo!
    27 Jan '05 13:16
    Hey! I thought we were supposed to use a balance! How on earth can you decide if it's 55, 54, 53, ... with a simple balance?
  5. Standard member Palynka
    Upward Spiral
    27 Jan '05 13:21
    Originally posted by TheMaster37
    Hey! I thought we were supposed to use a balance! How on earth can you decide if it's 55, 54, 53, ... with a simple balance?
    Put the coins on one side and put weights on the other side. Like in the markets...
  6. Standard member genius
    Wayward Soul
    27 Jan '05 14:41 / 1 edit
    ignore me - Palynka's idea works better and takes only one weigh...
  7. 28 Jan '05 04:52
    Originally posted by genius
    ignore me - Palynka's idea works better and takes only one weigh...
    It works if you are allowed to use standard weights and measures , along with the balance. If separate standard weights are not permitted then it cannot be done in a single " balancing" act.
  8. Standard member genius
    Wayward Soul
    28 Jan '05 12:38
    Originally posted by CoolPlayer
    It works if you are allowed to use standard weights and measures , along with the balance. If separate standard weights are not permitted then it cannot be done in a single " balancing" act.
    well-if you just have the scales you could weigh 5 bags against 5 and remove one bag from each side until both sides balance. when this happens, the bag you just removed from the formally lgihter side is the one your looking for! i thought it was quite an ingenius method, but then looked at playnka's worked better etc etc etc...but i still like mine cause i thought of it and meh!
  9. 28 Jan '05 14:12
    Originally posted by Palynka
    put 1 coin from the first sac, 2 from the second,..., 10 from the tenth.

    if all coins weighed the same this selection should weigh 55.

    If it weighs 54 it's the first, 53 it's the second...45 is the tenth.
    That's right!
  10. Standard member TheMaster37
    Kupikupopo!
    28 Jan '05 15:40
    Originally posted by yevgenip
    That's right!
    The original problem as stated did not mention any standard weights involved.

    Another solution could very well have been that you take two more balances, and weigh once on each of them. But that's simply cheating

    Be more specific in your questions!
  11. 28 Jan '05 17:26
    Originally posted by genius
    well-if you just have the scales you could weigh 5 bags against 5 and remove one bag from each side until both sides balance. when this happens, the bag you just removed from the formally lgihter side is the one your looking for! i thought it was quite an ingenius method, but then looked at playnka's worked better etc etc etc...but i still like mine cause i thought of it and meh!
    That's smart. A further improvement ,in terms of simplification, would be taking 10 coins from each of the 10 bags and place the coins from 5 bags on one side and those from the other 5 bags on the other side of the scale. Thereafter the procedure of collectively removing the coins of one bag at a time, could be done till balance , as in your procedure.