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Sunday Times Teaser 3113 – The Plumber’s Buckets

by Brian Gladman on May 20, 2022

by Peter Good

Published Sunday May 22 2022 (link)

A plumber was trying to empty a tank containing 100 litres of water using three buckets, each marked with a different whole number of litres capacity between 10 and 20 litres. He calculated that he could exactly empty the tank, but only by using all three buckets and completely filling each bucket a different number of times. He filled and emptied each bucket the calculated number of times but the tank still contained 6 litres of water, because the smallest bucket had a dent that reduced its capacity by 3 litres.

What were the marked capacities of the three buckets?

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4 Comments Leave one →
  1. Brian Gladman permalink

    Here is an alternative approach that allows a strict interpretation of the text to be applied.

    • Frits permalink

      @Brian,

      “but only by using all three buckets and completely filling each bucket a different number of times”. I read his that both conditions belong to the “but only” clause. In that case there is no valid solution.

      • Brian Gladman permalink

        Which is why I chose an interpretation in which it only covers the first condition.
        I doubt that the numbers in the teaser are wrong (100, 94 and 3) so I chose to
        put the error elsewhere. We will have to wait for the official answer to know
        (or a manual solver will find a better interpretation).

  2. GeoffR permalink

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