Question 64
Some of the lattice points $(x, y)$, with $1 \le x \le 101$ and $1 \le y \le 101$ are marked so that no 4 marked points form the vertices of an isosceles trapezoid with bases parallel to the $x$-axis or the $y$-axis (a rectangle is counted as an isosceles trapezoid). Determine the maximum number of marked points. (A lattice point is a point with integral coordinates.)