You may also like

problem icon


Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

problem icon

Russian Cubes

I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?

problem icon

N000ughty Thoughts

How many noughts are at the end of these giant numbers?


Age 14 to 16 Challenge Level:

example 1Exsample 2

A walk is made up of diagonal steps, starting at the bottom left and ending up back on the bottom line (x-axis). You can move diagonally up and down towards the right but you cannot move towards the left.

A diagonal must go from a left-hand corner of a square to the opposite right-hand corner of the same square.

The examples above all show 10-step walks. So let's look at a 2-step walk in more detail:

2-step walk

There is only one way to make a 2-step walk - from A up to x and down to B:

2-step walk with labels

Here are two 4-step walks:

4-step example 24-step example

Are there any more 4-step walks?

How do you know you have them all?

How many 6-step, 8-step walks are there?

Can you find a general rule?

See also the problems One Basket and Counting Binary Ops