Chapter 1 - Distribution Dilemmas

Summary

A Shepherd and his Sheep

Here is a classic puzzle.

An elderly shepherd died and left his entire estate to his three sons. To his first son, whom he favored the most, he bequeathed ½ his flock of sheep, to the second son ⅓, and to the third son, whom he liked the least, 1/9 of his flock. (Is there a problem with these proportions?)

Not wishing to contest their father's will, the three sons went to the pasture to begin divvying up the flock. They were alarmed to count a total of 17 sheep! Is there a means for the three sons to successfully carry out their father's wishes?

Taking it Further. Meanwhile, three daughters of a recently deceased shepherdess faced a similar dilemma. Their mother, very wealthy, but also possessing a flawed understanding of fractions, had bequeathed her estate of 495 sheep according to the proportions 1/5 to her first daughter, 1/33 to her second, and 1/2145 to her third! Can her will be successfully honored?

Iterated Sharing

A group of friends sits in a circle, each with a pile of wrapped candies. (Wrapped candy is used because each piece will be handled by many people before being eaten.) Some people have 20 or more pieces, others none, and the rest some number in between. The distribution is quite arbitrary except for the fact that everyone has been given an even number of pieces. A reserve supply is set aside.