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## 'Mathematical Swimmer' printed from http://nrich.maths.org/

### Why do this
problem?

This problem
involves calculating with fractions and also uses knowledge of
factors and multiples. It is a difficult problem that requires
clear and logical thinking.

### Key questions

How do you think you can start on this problem?

Would it help to make a list of some prime numbers?

Why not think of numbers which have many factors and try
them?

Would it help to make a list of numbers which have many
factors?

Why not start with $12$? What are its factors?

Are all the numbers up to $12$ either a prime number or a
fraction that will simplify?

Now do you think you can try with larger numbers?

### Possible extension

Learners could on to

Peaches Today, Peaches
Tomorrow.

### Possible support

If learners are finding coping with fractions are very difficult
suggest trying this Stage 2 problem,

Fractions Made
Faster or even

Fractional
Wall.