# 10 year retrospective - January 2007, All Stages

## Problems

### Domino Sorting

##### Stage: 1 Challenge Level:

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

### Overlapping Squares

##### Stage: 2 Challenge Level:

Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.

### Consecutive Numbers

##### Stage: 2 Challenge Level:

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### One to Fifteen

##### Stage: 2 Challenge Level:

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

### Square Tangram

##### Stage: 2 Challenge Level:

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

### Magic Matrix

##### Stage: 2 Challenge Level:

Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?

### It's a Tie

##### Stage: 2 Challenge Level:

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

### Isosceles Triangles

##### Stage: 3 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

### Triangles to Tetrahedra

##### Stage: 3 Challenge Level:

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

### Noughts and Crosses

##### Stage: 3 Challenge Level:

Ever thought of playing three dimensional Noughts and Crosses? This problem might help you visualise what's involved.

### 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?