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## 'What Is Ziffle?' printed from http://nrich.maths.org/

## What Is Ziffle?

There's a planet out in space called Zargon ........

On this planet these areĀ numbers that are called ziffles

These numbers are ziffles $56, 105, 28, 63, 49$

These numbers are not ziffles: $100, 18, 65, 9, 76$

Only two of these numbers are ziffles: $16, 14, 57, 24, 70$

So what is special about the ziffles?

### Why do this problem?

This short problem encourages children to look for patterns and apply knowledge of their times tables and of the properties of numbers.

Possible approach

Encourage the children to look at the sets of numbers in turn and explore their characteristics and properties.

Key questions

Are they all odd in one set and even in the other?

Are they prime numbers?

Are they triangle numbers?

Are they all in the five times table?

How about other tables?

Possible extension

Either you or your pupils could make up their own problem using, for example, multiples of $13$ or another table that they might like to practice.

Possible support

Take an easier table and develop sets of multiples and non multiples to identify.

Use concrete apparatus to explore divisibility such as Multilink cubes.