Secret Santa/Fixpointfree/Method/Paper/Exercise

There are ${}n\geq 4$ persons in a room and they would like to play secret Santa. This means that for each person ${}A$, another person ${}B\neq A$ has to be determined to whom ${}A$ has to give a gift. Every person is only allowed to know who to give the gift, no one is allowed to know more. The people stay the whole time in the room, they do not look away. They only have paper and pens. They are allowed to shuffle and to look in secret at choosen cards. Describe a procedure to determine a gift relation which satisfies all conditions.

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