MathDB

How many triangles appear in the diagram below: [asy] import graph; size(6cm); real lsf=0.5; pen dps=linewidth(0.6)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=0,xmax=8,ymin=0,ymax=8; draw((0,8)--(0,0)); draw((0,0)--(8,0)); draw((8,0)--(8,8)); draw((8,8)--(0,8)); draw((0,8)--(1,7)); draw((1,7)--(2,8)); draw((2,8)--(3,7)); draw((3,7)--(4,8)); draw((4,8)--(5,7)); draw((5,7)--(6,8)); draw((6,8)--(7,7)); draw((7,7)--(8,8)); draw((8,6)--(7,7)); draw((0,6)--(1,7)); draw((1,7)--(2,6)); draw((2,6)--(3,7)); draw((3,7)--(4,6)); draw((4,6)--(5,7)); draw((5,7)--(6,6)); draw((6,6)--(7,7)); draw((1,5)--(0,6)); draw((1,5)--(2,6)); draw((2,6)--(3,5)); draw((3,5)--(4,6)); draw((4,6)--(5,5)); draw((5,5)--(6,6)); draw((6,6)--(7,5)); draw((7,5)--(8,6)); draw((7,5)--(8,4)); draw((0,4)--(1,5)); draw((1,5)--(2,4)); draw((2,4)--(3,5)); draw((3,5)--(4,4)); draw((4,4)--(5,5)); draw((5,5)--(6,4)); draw((6,4)--(7,5)); draw((1,3)--(0,4)); draw((1,3)--(2,4)); draw((3,3)--(4,4)); draw((3,3)--(2,4)); draw((5,3)--(4,4)); draw((5,3)--(6,4)); draw((6,4)--(7,3)); draw((7,3)--(8,4)); draw((8,2)--(7,3)); draw((0,2)--(1,3)); draw((1,3)--(2,2)); draw((2,2)--(3,3)); draw((3,3)--(4,2)); draw((5,3)--(4,2)); draw((5,3)--(6,2)); draw((7,3)--(6,2)); draw((7,1)--(6,2)); draw((7,1)--(8,2)); draw((7,1)--(8,0)); draw((6,0)--(7,1)); draw((4,0)--(5,1)); draw((5,1)--(6,0)); draw((2,0)--(3,1)); draw((3,1)--(4,0)); draw((0,0)--(1,1)); draw((1,1)--(2,0)); draw((1,1)--(0,2)); draw((1,1)--(2,2)); draw((2,2)--(3,1)); draw((3,1)--(4,2)); draw((4,2)--(5,1)); draw((5,1)--(6,2)); dot((8,0),ds); clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); [/asy]

Problem Statement