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Ball
Task number: 3489
There are n couples at a ball. How many ways are there to divide everyone into pairs such that no couple dances together?
Solution
Dividing everyone into pairs corresponds to a bijective mapping f from {1,…,n} to the same set (e.g. the woman from the i-th couple will dance with the man from the f(i)-th couple).
We are interested in the mappings without a fixed point; this corresponds to the hat-matching problem from the lecture.
