### 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?

# Megabytes and Kilobytes

##### Age 14 to 16 ShortChallenge Level

Answer: $1 048 576$

Using powers
$2^{10}$ kilobytes in $1$ megabyte, and $2^{10}$ bytes in each of those $2^{10}$ kilobytes
So $2^{10}\times2^{10}$ bytes in $1$ megabyte.

$2^{10}\times2^{10}=2^{10+10}=2^{20}=1 048 576$, so there are $1 048 576$ (not $1 000 000$) bytes in a megabyte.

Using normal numbers
$2^{10}=1024$
$1024$ kilobytes in $1$ megabyte, and $1024$ bytes in each of those $1024$ kilobytes
So $1024\times1024$ bytes in $1$ megabyte.

$1024\times1024=1 048 576$, so there are $1 048 576$ (not $1 000 000$) bytes in a megabyte.

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