Here's another math puzzle for you, this one from the 16th or 17th century:

You have four (integral) weights (w_1, w_2, w_3, w_4) and a balance scale such that you can weigh any object weighing from 1 lb to 40 lbs (no fractions). The weights may go on either side of the scale (eg, with the object, or in the opposite pan). What are the w_i ?

Some background and the solution here: Bachet's Four Weights Problem.