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## 'Special Numbers' printed from http://nrich.maths.org/

### Why do this problem?

This problem provides a great opportunity to introduce a very
useful way of representing numbers algebraically.

### Possible approach

Present the learners with the problem displayed in the speech
bubbles. Give the class some time to look for special numbers -
once a few have been found, more will quickly follow. Once there is
a consensus that a family of special numbers has been found, bring
the class together and share what they think is going on. Ask them
"Are you sure you've found all the special numbers? How
could we be certain?" Suggest that an exhaustive search would be
exhausting!

Introduce the class to the algebraic representation of
two-digit numbers and work through the reasoning together to
establish that there are only nine solutions.

Then present the suggestions for other types of special
numbers, and challenge learners to predict, using algebra, which
numbers will be special for each type.

### Key questions

Can we use algebra to help us to understand what's going
on?

### Possible extension

### Possible support

For students who find the leap into algebra too difficult, the
problem can be used to offer an interesting numerical
challenge.