Math puzzle: A Loopy Holiday Gift Exchange

You are participating in a holiday gift exchange with a few classmates. You each write down your own name on a slip of paper and fold it up. Then all the students place their names into a single hat. Next, students pull a random name from the hat, one at a time. If at any point someone pulls their own name from the hat, the whole class starts over, with everyone returning the names to the hat. Once the whole process is complete, each student purchases a gift for the classmate whose name they pulled. Gifts are handed out at a big holiday party at the end of the

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