**Question**

**Introduction**

A
premier school in Singapore
is said to have set a question similar to this question in a regular school
test. I suspect it was meant to select
pupils to represent the school for mathematics Olympiad.

I present two solutions: one using the idea of

I present two solutions: one using the idea of

*prime factor*, the other one using the possible*factorisation*of some number into two factors.**Solution 1**

**Solution 2**

**Remark**

The
Factorisation Grid helps us to perform the factorisation. It is presented in the form that I learned
it, in which the cross terms are written in the middle. I prefer it this way. Nowadays, the textbooks and the schools put
these terms on a column on the right instead of in the middle.

The word “unity” in
mathematics is just a fancy word for the number
1. It is a “partition” because
the number is being split into two separate parts (fractions). The “partition of unity” concept can be
extended, and is useful in advanced mathematics including signal processing, weighted
averages, spline functions and topology.**Suitable Levels**

* Lower Secondary
Mathematics Olympiad

* any student who
loves a challenge in algebra or number theory

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