You may also like

problem icon

Maze 100


problem icon

Delia's Routes


problem icon

Snails' Trails


Watch Your Feet


Watch Your Feet

Have you ever read a Winnie the Pooh poem called "Lines and Squares" by A.A. Milne? It tells us how Christopher Robin plays a game with himself as he walks along pavements, trying not to walk on the "lines" (the edges of the paving stones).

Have you ever done this? I know I have! This investigation is based on a similar idea - but here I want to walk on the lines!

This is a picture of the path leading up to my front door from the road:


I like to walk along the cracks of the paving stones, but not the outside edge of the path itself because I may tread on the grass.

The only way I can do it is by walking straight down the middle of the path like this:

If the path were three paving stones wide instead of just two it would look like this:

Remembering that I can only walk along the sides of the paving stones and I mustn't tread on the outside edge, how many different routes can you find for me to take? (By the way, you must not turn back on yourself, and you must head towards the door or sides - so you cannot walk towards the road on your journey.)

Do any of your routes have a repeating pattern?

Imagine now that the path is even wider, with four paving stones:

What different routes can you find now?

Perhaps you could group them into those with a repeating pattern and those without. Maybe you can find other ways to group the routes.

If I could also take steps diagonally across a paving stone, like this:

then there are even more possibilities. Try to find the new routes yourself, starting with 3 paving stones width. Remember all the same rules apply as before.

Why do this problem?

This problem will give opportunities for pupils to develop spatial awareness as well encouraging a logial approach to solving the challenge. There is also the opportunity for pupils to explore different ways of recording.

Getting the pupils interested by talking about many children's habit in some countries of not walking on the cracks will lead well into this exploration.

Key questions

Can you tell me about why you chose this route?
Can you find a different route?
How will you record what you've done?

Possible extension

Learners could explore what happens when the path has a right angle turn or two.

Possible support

Squared paper and/or simple drawing programs may be useful.