# Special Numbers Poster

Special Numbers Poster

## Problem

This poster is based on the problem Special Numbers.

The poster is available as a PDF, or the image below can be clicked on to enlarge it.

Image

## Student Solutions

**Answer**: No, but we know that your number ends in a 9 (one of 19, 29, 39, ...)

Why?

If the number is written $ab$, then the number is $10a+b$

$a\times b + (a+b) = 10a + b \Rightarrow ab + a = 10a$

$ab + a = (b+1)a$ so $b+1=10\Rightarrow b=9$ (or $a=0$)

But then $a$ could be anything!