MathDB
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 4×4=164\times 4 = 16 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 100×100100\times 100 points.