A long time ago some ancients needed to make 5 weights that could weigh any amount of weight up to 121 grams.

The ancients though, had only a 1 gram weight and 120 grams of clay(which they would later make into weights. So with only a scale, 120 grams of clay and a 1 gram weight how would you create all the other weights needed to weigh any amount up to 121 grams?

What is the minimum amount of weighings required to do this?

(In reply to solution ? by Keedom)

I take it you mean that you create a 60-g weight by evenly dividing the 120 g, then a 30-g weight by evenly dividing one of the 6--g weights, etc.

However, with the now-produced set of weights being 60, 30, 15, 8 and 7, you wouldn't have anything to weigh out, say, 3 grams.

The idea is to get the 5 weights that were specified in the 5 Weights problem: 1, 3, 9, 27 and 81. These enable you from then on to weigh any integral number of grams from 1 up to 121. The 1-g weight is already present and is one of the five.

Posted by Charlie on 2003-03-26 08:14:52