The traditional way of putting names in a hat often fails because, its likely that someone will end up drawing their own name and the draw has to be done again. Also, due to the fact that there are limited successful draws, the draw isn't ever fair..
If you want a better explaination, watch this cool video. The Problems with Secret Santa
The solution is a derangement. We randomly select pairs of numbers, and then each person picks a pair, saying what number they are and who they are buying for.
No one can ever pick themselves and the draw never fails. Each person writes their name of the draw sheet. When the names are all written on each person knows who they are buying for.
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