## Sunday, December 20, 2015

### [OlymLS_20151220INEQ] An Egyptian Fraction Partition of Unity?

Problem

Introduction
This question appeared in a “holiday homework” from an IP school.  It is not the usual type of question in exams and tests, but it is a good mental-stretching exercise.  It is asking us to split unity (the number “1”) into three unit fractions (a.k.a. Egyptian fractions).
The first part can be solved by trial and error or “guess and check”.  The second part, proving that this is the only solution (are there any other solutions?), seems challenging.  We can solve this by making suppositions and using inequalities.

Solution

H03. Make a systematic list
H05. Work backwards
H07. Use guess and check
H08. Make suppositions  [ which may lead to negative conclusions ]
H10. Simplify the problem
H11. Solve part of the problem
H13* Use Equation / write a Mathematical Sentence

Suitable Levels
Primary School / Lower Secondary Olympiad
* other syllabuses that involve fractions and inequalities
* any learner who is itching for a mental challenge