NRICH: Route to Infinity

Can you describe this route to infinity? Where will the arrows take you next?

Take some time to look at the route followed by the arrows in this diagram. (Interactive)
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 1000th to be visited?

Age 11 to 14


Algebra & Pre-Algebra, Coordinates, Deductive Reasoning & Logical Thinking
Middle School, High School, Educator

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NRICH (University of Cambridge)

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Online Interactive Activity

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Click here for a poster of this problem.