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Definitely had to get some inspiration from what had already been posted on this one. I'm not sure if the logic is flawless, but it seems to have worked. Let me know if you see places where I can improve on this one!
I think the example output given is wrong, according to the answer only 25 people would get a present. My solution gives everyone (All 50) a present with no double pairings. (Used unique tool at end to check).