Experiment-conjecture-prove - February 2008, All Stages

Problems

problem Icon

Repeating Patterns

Stage: 1 Challenge Level: Challenge Level:1

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

problem Icon

Animated Triangles

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem Icon

Triangle Shapes

Stage: 1 and 2 Challenge Level: Challenge Level:1

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

problem Icon

Putting Two and Two Together

Stage: 2 Challenge Level: Challenge Level:1

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?

problem Icon

Triangle Relations

Stage: 2 Challenge Level: Challenge Level:1

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

problem Icon

Triangular Faces

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem Icon

9 Weights

Stage: 3 Challenge Level: Challenge Level:1

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?

problem Icon

Notes on a Triangle

Stage: 3 Challenge Level: Challenge Level:1

Can you describe what happens in this film?

problem Icon

Conway's Chequerboard Army

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem Icon

Equal Equilateral Triangles

Stage: 4 Challenge Level: Challenge Level:1

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

problem Icon

The Square Hole

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

problem Icon

Road Maker

Stage: 5 Challenge Level: Challenge Level:1

Which of these roads will satisfy a Munchkin builder?

problem Icon

Impossible Square?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Can you make a square from these triangles?

problem Icon

Impossible Triangles?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Which of these triangular jigsaws are impossible to finish?

problem Icon

Road Maker 2

Stage: 5 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you work out where the blue-and-red brick roads end?

Elsewhere...