A certain tribe had an interesting kind of annual festival, in which every male member of the tribe (regardless of age) had to contribute a levy of grain into the tribal store. Their unit of weight was roughly the same as our pound avoirdupois, and each tribesman had to contribute one pound of grain for every year of his age.
The contributions were weighed on the tribe's ceremonial scales, using a set of seven ceremonial stones. Each of these weighed an integral number of pounds, and it was an essential part of the ritual that not more than three of them should be used for each weighing, though they need not all be in the same pan.
If ever a tribesman lived to such an age that his contribution could no longer be weighed by using three or fewer stones, the levy of grain would terminate forever. And in the previous year, one old man had died only a few months short of attaining this critical age, greatly to the relief of the headman of the tribe.
It has been determined that the stones can measure the maximum age. What is this age and what were the weights of the seven ceremonial stones?
Well, I figure that if the seven stones weigh 1, 2, 3, 7, 10, 34, and 61 pounds, you can measure any weight from one up to 74 pounds using just three stones (making the "maximum age" 74 years old).
This is probably not optimal - it appears that you should be able to stretch out the beginning of the sequence a little more (1, 2, 3, 7, 10 seems redundant) but they come in handy so I'm not sure. I'll see if I can come up with something better.
Edited on November 14, 2006, 1:56 pm
Posted by tomarken
on 2006-11-14 13:55:29