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The damaged scale

The damaged scale

We want to weigh exactly ten kilos of sugar. For this we have two weights of five kilos each and a scale with two dishes that is unbalanced. This means that, without there being any weight on either of the two dishes, there is one that is higher than the other.

How exactly would you weigh the 10 kilos of sugar?

Solution

We put the two weights of 5 kilos each on one of the dishes. We pour sugar on the other scale plate until both are at the same height. Now we remove the two weights and pour sugar in place until the saucers are again at the same height. The sugar we put in the dish where the two weights were weighs exactly the same as the weights themselves, that is: 10 kilos.