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Route to Infinity

Age 11 to 14 Challenge Level:

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.