PROBLEM # 1
The founders of Hairytown decreed years ago that:

1. No two people can have the same number of hairs
2. No one can have 999 hairs.
3. No one can have more than, or the same number of hairs as, the population of the town


PROBLEM #2

You intend to fly non-stop around the world.  But you can only go halfway around the world on a full tank. However you can arrange many planes exactly like yours to assist with refuelling. Assuming refuelling can be done midair, ignoring refuelling and turning time, and without crashing any plane, what is the minimum number of planes you will need?


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Find the value of the infinite product

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