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Challenge 333: A Sum for Santa

Santa’s top team of 101 elves have been called in to deliver some last-minute presents. Each elf picks up at least one present to deliver, and then goes to Santa’s briefing room where the elves sit in a circle to wait for further instructions.

Every one of the 300 presents to be delivered have been picked up by one of the elves.

Emmy, a mathematically minded elf, claims that however the presents were shared out between the elves, it would always be possible to find a group of elves all sitting in adjacent places in the circle who have picked up exactly 200 presents between them.

Prove that Emmy is correct.