Copyright © University of Cambridge. All rights reserved.

## 'Walkabout' printed from http://nrich.maths.org/

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:

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

Here are two 4-step walks:

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