### 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?

# Root 2017

##### Age 14 to 16 ShortChallenge Level

Squaring numbers to get close to $2017$
$40^2=1600$ too small
$50^2=2500$ too big, so $\sqrt{2017}$ is between $40$ and $50$.
$45^2=2025$, very close but a bit too big
$44^2=1936$, too small, so $\sqrt{2017}$ is between $44$ and $45$.