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# Route to Infinity

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Age 11 to 14

Challenge Level

*Route To Infinity printable sheet*

Take some time to look at the route followed by the arrows in this diagram.

Then look away and describe the path to a friend.

If the pattern of arrows continues for ever, which point will the route visit immediately after (18,17)? Explain how you know.

How many points will be visited **before** the route reaches the point (9,4)?

Explain how you worked it out.

Which point will be the $1000^{th}$ to be visited?

Click here for a poster of this problem.

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

This article looks at the importance in mathematics of representing places and spaces mathematics. Many famous mathematicians have spent time working on problems that involve moving and mapping things.

Have you ever wondered how maps are made? Or perhaps who first thought of the idea of designing maps? We're here to answer these questions for you.