# Experiment-conjecture-prove - February 2008, All Stages

## Problems

### Repeating Patterns

##### Age 5 to 7 Challenge Level:

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

### Animated Triangles

##### Age 5 to 7 Challenge Level:

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

### Triangle Shapes

##### Age 5 to 11 Challenge Level:

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

### Triangle Relations

##### Age 7 to 11 Challenge Level:

What do these two triangles have in common? How are they related?

### Putting Two and Two Together

##### Age 7 to 11 Challenge Level:

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

### Triangular Faces

##### Age 7 to 11 Challenge Level:

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

### Notes on a Triangle

##### Age 11 to 14 Challenge Level:

Can you describe what happens in this film?

### 9 Weights

##### Age 11 to 14 Challenge Level:

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

### Conway's Chequerboard Army

##### Age 11 to 14 Challenge Level:

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

### Equal Equilateral Triangles

##### Age 14 to 16 Challenge Level:

Using the interactivity, can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

### The Square Hole

##### Age 14 to 16 Challenge Level:

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

##### Age 14 to 18 Challenge Level:

Which of these roads will satisfy a Munchkin builder?

### Impossible Triangles?

##### Age 16 to 18 Challenge Level:

Which of these triangular jigsaws are impossible to finish?

### Impossible Square?

##### Age 16 to 18 Challenge Level:

Can you make a square from these triangles?