What is the optimal number base from the point of view of an old-fashioned typesetter?
In other words, for a typesetter to be prepared to set an arbitrary number from 0 up to 7^100 using base 7, he would need to have on hand 100 zeros, 100 ones, 100 twos, etc. for a total of 700 pieces of type. How many pieces of type would he need to have on hand to be able to set an arbitrary number in the same range, using a different base? Presumable the typesetter wishes to minimize his purchase of type, so which base would be best from his point of view?
FWIW, this is a problem my brother showed me many years ago when we were in high school. I had the impression that he invented the problem, but I'm not certain that's the case.