Maths prize for 3 November 2015: weighing

justice-scales-22215416

You have a scale with two pans, so for example you can measure 2 grams exactly by putting a one-gram weight in one pan and a three-gram weight in the other. With what four weights can you measure any weight up to 40 grams? With what five can you measure any weight up to 121 grams?

(Hint: start with a simplified version of the problem. With which two can you measure any weight up to 4 grams? With which three can you measure any weight up to 13 grams?)

Prize: 200 Vivos and a Freddo for a successful answer and a good attempt at an explanation. Answers to Mr Osborn or Mr Thomas by Assembly on Tuesday 3 November.