Question 105
Consider a grid formed by 49 points, which are the vertices of the 36 squares of side 1 into which a square of side 6 is divided.
We say that a square with vertices at points of the grid is good if its sides and its diagonals do not lie on the sides of the squares of the grid.
a) Find the number of good squares that can be formed with vertices at points of the grid.
b) Show that there exist two good squares that are disjoint and non-congruent, such that the smallest distance between their points is $\frac{\sqrt{5}}{5}$.
We say that a square with vertices at points of the grid is good if its sides and its diagonals do not lie on the sides of the squares of the grid.
a) Find the number of good squares that can be formed with vertices at points of the grid.
b) Show that there exist two good squares that are disjoint and non-congruent, such that the smallest distance between their points is $\frac{\sqrt{5}}{5}$.