TITLE: Odd "How many triangles are there in the picture?" Question From the First Stage of Israel's International Mathematical Olympiad Selection Process
QUESTION [5 upvotes]: So stage 1 of of Israel's International Mathematical Olympiad selection process took place on Monday, and this was one of the questions (6 or 7 out of 10).
Q:
(The way the shape is produced wasn't inscribed, but its a pretty easy guess):
Draw an interval from each vertex of a square to the 2 midpoints of the sides it is not on.
How many triangles are there in the shape?

Is there a (viable) way to solve questions similar to the one I showed?

REPLY [4 votes]: You can follow this picture, the number of triangles are written inside of each drawing: