Chapter 4, Problem 61E

Exercises 61 and 62 are based on the following story: Mom found an open box of her children's favorite candy bars. She decides to apportion the candy bars among her three youngest children according to the number of minutes each child spent doing homework during the week.

a. Suppose that there were 11 candy bars in the box. Given that Bob did homework for a total of 54 minutes, Peter did homework for a total of 243 minutes, and Ron did homework for a total of 703 minutes, apportion the 11 candy bars among the children using Hamilton's method.

b. Suppose that before mom hands out the candy bars, the children decide to spend a “little” extra time on homework. Bob puts in an extra 2 minutes (for a total of 56 minutes), Peter an extra 12 minutes (for a total of 255 minutes), and Ron an extra 86 minutes (for a total of 789 minutes). Using these new totals, apportion the 11 candy bars among the children using Hamilton's method.

c. The results of (a) and (b) illustrate one of the paradoxes of Hamilton's method. Which one? Explain.