St. Petersburg Mathematical Olympiad Problem 2
Ten points, labelled
to
are chosen in the plane. Permutations of
are obtained as follows: for each rectangular coordinate system in which the ten points have distinct first coordinates, the labels of the points are listed in increasing order of the first coordinates of the points. Over all sequences of
labelled points, what is the maximum number of permutations of
obtained in this fashion?
The answer is 90.
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