Question 31
A square of side $5$ is divided into $25$ unit squares by means of lines parallel to the sides. Let $A$ be the set of $16$ interior points, which are vertices of the unit squares, but which are not on the sides of the initial square.
What is the greatest number of points in $A$ that can be chosen such that any three of them are not vertices of an isosceles right triangle?
What is the greatest number of points in $A$ that can be chosen such that any three of them are not vertices of an isosceles right triangle?