Wednesday, October 27, 2010

coin weighing

There are   10 piles containing large number of coins. Coins in same pile all weigh same but may differ from coins in other piles. It is given that all  coins weigh 1 gram, 2 gram or 3 gram. You have a digital weighing machine, to measure any weight. You can pick as many coins as you wish from the piles.How will you ascertain weight of all coins in minimum number of weighments.
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3 comments:

  1. VipulFebruary 19, 2011 at 11:19 AM

    Hi Gaurav,

    Could you please post the solution of this problem?

    Thanks,
    Vipul

    ReplyDelete
  2. cheraFebruary 20, 2011 at 11:05 AM

    one weighing is enough to find weights.

    choose 1 coin from 1st pile, 10 from second pile, 100, from third pile and so on, i.e. 10^9 coins from last pile.

    measure this selection on weighing machine.
    if the weights of coins are w1,w2,...,w10.

    then total weight= w1+10W2=1000w3+...+10^9w10.
    so weights wi are just digits of the total weight in base 10.

    pl. note that instead, u can choose 1,4,16,...4^9 coins. then the total weight expressed in base 4 , will yield the coin weights.

    ReplyDelete
  3. plantfoodfan24June 14, 2020 at 3:09 AM

    Load cells are used today to weigh industrial applications but this hasn't always the case. Before load cells mechanical lever scales were used. load cell

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