AN EGYPTIAN FRACTION

Imagine overseeing a farm. Distribute 29 equal sacks of grain evenly to 45 people. There is only one sorting table, so you can't divide up more than one sack at a time. How can you assure a fair share for each person?
Consider this: 1/3 + 1/5 + 1/9 = 29/45. So, 15 of the sacks can be divided into 3 parts, 9 of them into 5 parts, and 5 of them into 9 parts. Then, each of the 45 people gets one of each type of part. In the diagram below, each person gets a red, yellow, and green part.

Figure 1. Dividing 29 sacks equally between 45 people. Each person gets