# 10 year retrospective - January 2007, Stage 4&5

## Problems

### More Number Pyramids

##### Stage: 3 and 4 Challenge Level:

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

### Big Powers

##### Stage: 3 and 4 Challenge Level:

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.

### One Basket or Group Photo

##### Stage: 2, 3, 4 and 5 Challenge Level:

Libby Jared helped to set up NRICH and this is one of her favourite problems. It's a problem suitable for a wide age range and best tackled practically.

### Nine Colours

##### Stage: 3 and 4 Challenge Level:

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

### Fac-finding

##### Stage: 4 Challenge Level:

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

### Three by One

##### Stage: 5 Challenge Level:

There are many different methods to solve this geometrical problem - how many can you find?

### All about Ratios

##### Stage: 5 Challenge Level:

A new problem posed by Lyndon Baker who has devised many NRICH problems over the years.

### Gold Yet Again

##### Stage: 5 Challenge Level:

Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."