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3. Induction step: Prove true for n = k + 1. So we must prove that in a
line of k + 1 people in which a woman is in front and a man in back, that
somewhere in this line we have a woman directly in front of a man. So
let a woman be in ﬁrst place and a man in last place. Now consider the
penultimate person. This person is either a woman or a man. So we
have two cases.
(a) Case I: The penultimate person is a woman. Then she is directly
in front of the man last in line. So in this case, we have a woman
directly in front of...
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