# Your Solutions - Stage 4 & 5

### Tens

##### Stage: 5 Challenge Level:

When is $7^n + 3^n$ a multiple of 10? Can you prove the result by two different methods?

### Giants

##### Stage: 5 Challenge Level:

Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?

### Going to the Cinema

##### Stage: 3 and 4

A cinema has 100 seats. Is it possible to fill every seat and take exactly £100?

### You Can't Make an Omelette...

##### Stage: 3 and 4

Can you devise the most efficient strategy for finding the highest floor from which you can drop an egg safely?

### Climbing the Stairs

##### Stage: 3 and 4

In how many ways can I get upstairs?

### Combining Lengths

##### Stage: 3 and 4

How many different lengths is it possible to measure with a set of three rods?