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?

The posted solution requires 8 weighings even when it is assumed that the ancients knew they had 120 grams of clay to begin with. My first comment on this puzzle shows that with this assumption, the 5 weights can be produced in 6 weighings.

In the second step, after using the 1-g and 3-g weights together to measure out 4 g of clay, instead of weighing out another 4 g of clay and then another 1 g of clay, just use the original 1-g weight with the first 4 g measured to get 5 g of clay in one step. Then combine the 4+5 into a 9-g weight, rather than 4+4+1.

Likewise, to get the 27-g weight just weigh out 13 grams once (not twice), then measure out 14 grams using the 1-gram weight and the 13 grams of clay on one side, and combine the 13+14 to get a 27-gram weight.

Then with the assumption that these ancients actually KNEW they had 120 grams of clay, it's done with only 6 weighings, rather than 8.

But how did these ancients actually know they had 120 grams of clay to begin with?

Posted by Charlie on 2003-03-30 06:19:56