Gunga P8
Source:
October 16, 2021
MOAA 2021Gunga
Problem Statement
Compute the number of triangles of different sizes which contain the gray triangle in the figure below.[asy]
size(5cm);
real n = 4;
for (int i = 0; i < n; ++i) {
draw((0.5*i,0.866*i)--(n-0.5*i,0.866*i));
}
for (int i = 0; i < n; ++i) {
draw((n-i,0)--((n-i)/2,(n-i)*0.866));
}
for (int i = 0; i < n; ++i) {
draw((i,0)--((n+i)/2,(n-i)*0.866));
}
filldraw((1.5,0.866)--(2,2*0.866)--(2.5,0.866)--cycle, gray);
[/asy]Proposed by Nathan Xiong