Beach Day by Rodger Bliss
May 2024

The Counterfeit Coin

You have nine coins. One of the nine is counterfeit. The counterfeit coin can only be
distinguished by weight—it is slightly heavier than the rest. Using a balance scale what’s the least amount of weighings to find the counterfeit coin.

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5 guesses to The Counterfeit Coin

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  • the least amount of weight is 1/16 of a ounce

  • dude

    Nope, that’s not it.

    We’re looking for the least amount of weighings to find the counterfeit coin.

    Keep trying!

  • Roolstar

    2 weighings would be enough:

    Just divide the nine coins in 3 groups of 3 coins each A, B & C

    Weighting 1: Compare A & B
    If one of them is heavier Take it to Weighing 2, if not, take C to weighing 2

    Weighing 2: Compare 2 coins from that group
    If one of them is heavier, you found it, if not, it’s the 3rd coin not on the scale.

  • Roolstar

    How many weighings are needed to find the counterfeit coin in a 27 coins group?
    How about 81?

  • You nailed it, Rool!

    Create three groups of three coins. Groups 1, 2 and 3. Balance Group 1 against Group 2.(weighing #1)
    If the two groups balance, the bad coin is in Group 3. If one group of coins weighs more than the other, the bad coin is in the heavier group.

    Once you have determined which group contains the counterfeit coin, take any two coins
    from the bad group and weigh them against each other (weighing #2). If they weigh the same, the bad coin is the third coin. Otherwise the bad coin is the heavier coin of the two.
    You’re today’s winner!!!