June 2014
Problem of the Month

Euclid's Problem

Euclid was supposed to have given the following problem in his lectures at Alexandria:

A mule and a donkey were going to the market laden with wheat.

The mule said, "If you give me one measure, I should carry twice as much as you, but if I give you one, we should have equal burdens.

What were their burdens?

Solution to the Problem:

The answer is 7 and 5 measures.

Let x = Number of measures of wheat the mule carries.
Let y = Number of measures of wheat the donkey carries.
Then x + 1 = 2(y - 1)
and x - 1 = y + 1
So, x + 1 = 2y - 2
and -x + 1 = -y - 1
Adding these last two equations, we get 2 = y - 3, so y = 5
Substituting back, we get x - 1 = 5 + 1, so x = 7.

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Chad Fore	Gate City, Virginia
3. Michal Hendrysiak	Tczew, Poland

Send any comments or questions to: David Pleacher