Q: Draw a regular hexagon, and connect every pair of vertices except one. The pair you don't connect are not on opposite sides of the hexagon, but along a shorter diagonal. How many triangles of any size are in this figure?The diagram in the upper right should help. I've removed one diagonal. It looks like a cool cube, don't you think?
Edit: The words "cool cube" were a double hint. First, the diagram I drew reminded me of the isometric cubes in the Q*Bert video game which was released in 1982. Additionally, if you cube the answer (82^3) you get 551368. I think the result is cool because 55+13=68. As a final clue, in several of my comments, I used the word "lead" which happens to be 82 on the Periodic Table of Elements.
A: 82 Triangles - be sure to watch the video for an explanation of the answer.