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## 'Route to Infinity' printed from http://nrich.maths.org/

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?

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