### Big Powers

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

### Rooted Via 10

How many of the numbers shown are greater than 10?

### Largest Expression

Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?

# Two in a Million

##### Age 14 to 16 ShortChallenge Level

Answer: $2^6$

$2$ is a factor of $10$, and $1000000=10^6$
$=(2\times5)^6$
$=2^6\times5^6$
$=2^6\times$ an odd number
So the highest power of $2$ that divides $1000000$ is $2^6$

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