Question 134
In Paircity there are $n \ge 2$ married couples numbered from $1$ to $n$. On New Year's Eve, each man congratulated two women from couples whose numbers differ by one. It turned out that for any two men from couples whose numbers differ by one, there is a woman who received congratulations from both of them.
Prove that at least one man congratulated his wife.
Prove that at least one man congratulated his wife.