no of different squares in a lattice of 100x100 points
Source: 2020 Chile National Olympiad level 2 p2
October 22, 2022
combinatoricscombinatorial geometry
Problem Statement
The points of this lattice points can be vertices of squares. [asy]
unitsize(1 cm);int i, j;for (i = 0; i <= 3; ++i) {
draw((i,0)--(i,3));
draw((0,i)--(3,i));
}draw((1,1)--(2,2)--(1,3)--(0,2)--cycle);for (i = 0; i <= 3; ++i) {
for (j = 0; j <= 3; ++j) {
dot((i,j));
}}
[/asy]Calculate the number of different squares that can be formed in a lattice of points.