# Powers and Roots

### Sissa's Reward

##### Stage: 3 Challenge Level:

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

### Power Countdown

##### Stage: 4 Challenge Level:

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

### Generating Triples

##### Stage: 4 Challenge Level:

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

### Power of 3

##### Stage: 4 Short Challenge Level:

What power of 27 is needed to get the correct power of 3?

### Megabytes and Kilobytes

##### Stage: 3 Short Challenge Level:

How many bytes are there in one megabyte?

### A Question of Scale

##### Stage: 4 Challenge Level:

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

### Sticky Numbers

##### Stage: 3 Challenge Level:

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Given these equations with unknown powers $x$ and $y$, can you work out $xy$?