[This may be the wrong SE for this question. But as a non-mathematician I feel it may be too simple for MathOverflow, and that I might benefit from a school-level explanation. Also, it might make a fun seasonal class assignment.]
If everyone in a classroom is involved in a Secret Santa style present exchange then, intuitively, it seems to make sense that it requires an even number in order to be fair. Someone gives a present, another receives: that's a pair. If there's an odd number in the class, someone will lose out.
Except they won't. Let there be three people in the class: pupils A, B and C. A gives to B, B gives to C, C gives to A.
In terms of "common sense" thinking this appears to be a paradox. Obviously it isn't. Can someone explain why not, mathematical terms?