[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

                                              

Heuristics Used

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