Half an Egg Wonder

Outline Mathematics
Word Problems

At first sight, this ancient problem may seem incongruous as it involves half an egg. But do try to solve it:

 

A peasant woman came to a market to sell some eggs. A first buyer took half her eggs plus 1/2 an egg. The same happened with the remaining eggs: a second buyer buyer took half her eggs plus 1/2 an egg. A third only bought what was left over: 1 egg.

How many eggs were there initially?

Solution


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Copyright © 1996-2012 Alexander Bogomolny

Solution

 

A peasant woman came to a market to sell some eggs. A first buyer took half her eggs plus 1/2 an egg. The same happened with the remaining eggs: a second buyer buyer took half her eggs plus 1/2 an egg. A third only bought what was left over: 1 egg.

How many eggs were there initially?

(In the applet below, click on the underlined omitted expressions. See what happens.)

// formulations

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.


References

  1. Ya. I. Perelman, Fun With Maths and Physics, Mir Publishers, 1988

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