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


|Up| |Contact| |Front page| |Contents| |Algebra|

Copyright © 1996-2017 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?

The problem is best solved by working out backwards from the end. After the second buyer bought half the remaining eggs plus 1/2 an egg, only 1,1,1/2 egg has been left over. Accordingly, this egg plus 1/2 egg constituted half the eggs she had before the second sale. Thus before that sale she had 3,1/2,1 1/2,3,3 1/2 eggs. This 3 plus 1/2,1,1/2 egg formed half the eggs she had before the first sale. This gives the answer: she started out with 7,6,7,8,9,10 eggs.

What if 1 egg was left over after 3 analogous sales? How many would have she started with?

We'd have to add 1/2 an egg to the previous amount of 7,6,7,8,9,10 and multiply the result by 2,1/2,2,3. She would have started with 15,12,13,14,15,16 eggs.

References

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

Related material
Read more...

  • Outline Mathematics: Crab's Weight
  • Diluted Paint
  • Five Siblings: an outline solution to a simple word problem
  • How old is Al?
  • Outline Mathematics: How old is Karen?
  • Lemons by Dozen

  • |Contact| |Front page| |Contents| |Algebra|

    Copyright © 1996-2017 Alexander Bogomolny

     62685713

    Search by google: