Radio Astronomy Systems Research Group

Take one coin from the first box, two from the second, three from the third, four from the fourth and five from the fifth.

Weigh all of these coins together. If all of the coins weighed 10 grams, you should have a total of 150 grams on the scale. If you take the total weight as reported by the scale and subtract off 150 grams, you will be left with some number between 1 and 5. This number corresponds to the box containing the heaver coins.