### Burning Down

One night two candles were lit. Can you work out how long each candle was originally?

### Percentage Unchanged

If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage is the width decreased by ?

### Digit Sum

What is the sum of all the digits in all the integers from one to one million?

# Powerful 9

##### Age 14 to 16 ShortChallenge Level

Answer: $9$

Look at the last digits of powers of $9$.

odd                     even
$9$                          $81$
$729$                    $279\times 9 = ....1$
$...1\times9=...9$        $...1$
$...9$                      $...1$

$9^9$ is a power of $9$ so $9^9$ is odd
This means that $9^{9^9}$ is an odd power of $9$, so it ends in $9$.

You can find more short problems, arranged by curriculum topic, in our short problems collection.