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    • Mathematical puzzle: find the authentic pieces
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    Mathematical puzzle: find the authentic pieces

    Pabio Posted on

    Thirty €1 coins are arranged in a circle on a table. Ten of these coins are fake and a little lighter than the 20 real coins. You don’t know where the fake pieces are in the circle, but you have been told that they are all directly next to each other in the circle. Your task is to find as many real coins as possible. To do this, you have at your disposal a beam balance, a device that allows you to compare the masses of two objects or sets of objects. Your beam scale has no weight and can only be used once. What coins should you weigh and how many real coins can you definitely find?

    You will be able to find at least 11 authentic pieces. To do this, start anywhere and number the pieces clockwise around the circle. Place part 1 on the left pan of the beam balance and part 11 on its right pan.

    If the pans remain in balance, both pieces must be genuine because there are only 10 fake pieces, all in a row. And since there are only 20 genuine coins, and you’ve already found two, the 19 coins in the clockwise segment from coin 12 to coin 30 cannot all be found. be authentic: the sequence of 10 fake coins must be included in this range. Thus, all 11 exhibits, from exhibit 1 to exhibit 11, are authentic.

    If the left board goes down, piece 1 is genuine and piece 11 is fake. Fake coins can only be included in the range from exhibit 2 to exhibit 20. Therefore, all 11 coins from exhibit 21 to exhibit 1 are genuine.

    And finally, if the right board sinks, piece 11 is authentic and piece 1 is fake. Fake coins can only be included in the range from exhibit 22 to exhibit 10. Therefore, all 11 coins from exhibit 11 to exhibit 21 are genuine.

    We would love to hear from you! Send us an email to [email protected] to share your experience.

    This puzzle originally appeared in Spektrum der Wissenschaft and has been reproduced with permission.

    Pabio
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