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Age 11 to 14 Short Challenge Level:

The diagram shows that $1 + 3 + 5 + 7 + 5 + 3 + 1 = 3^2 + 4^2$.

What is $1 + 3 + 5 + \dots + 1999 + 2001 + 1999 + \dots + 5 + 3 + 1$?


If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.