How many triangles are there in a three by three grid?

Answer 1

9 squares = 18 triangles

* * * * *

The correct answer is 76.

There are 9 points in the grid. You can pick any 3 out of these 9 points in 9*8*7/(3*2*1) = 84 ways.

However,

3 will form horizontal lines in the grid,

3 will form vertical lines in the grid, and

2 will form diagonal lines in the grid.

None of these 8 triplets will form triangles, but all the rest will.

So the answer is 84-8=76.