Question 9
A triangle $ABC$ has unit area. The first player chooses a point $X$ on side $AB$, then the second player chooses a point $Y$ on side $BC$, and finally the first player chooses a point $Z$ on side $CA$. The first player tries to arrange for the area of $XYZ$ to be as large as possible, the second player tries to arrange for the area to be as small as possible. What is the optimum strategy for the first player and what is the best he can do (assuming the second player plays optimally)?