Q: From Sam Loyd, a puzzle-maker from a century ago: Draw a 4x4 square. Divide it into 16 individual boxes. Next, draw a diagonal line from the middle of each side of the square to the middle of the adjoining side, forming a diamond. And, finally draw a long diagonal line from each corner of the square to the opposite corner, forming an X.Getting the answer is really easy; the key is to think of geometry. Let's see, if you start with a square and cut it along the diagonal, you get a triangle. Similarly, if you take a circle and cut a chord through the center, you get a semicircle. Take the measure in radians extended by the measure in degrees and you should have the answer, assuming you haven't made an error. Well, at least that is how I got my answer.
How many triangles can you find in this figure?
P.S. The NPR website currently has a couple typos in their posted puzzle (e.g. It should be Sam Loyd not Sam Lloyd. And a 4x4 square forms 16 smaller squares instead of 6. I'm pretty sure I have the intended question but be prepared for changes if the on-air puzzle is stated differently.
P.P.S. I've added a diagram now that I've confirmed the wording of the on-air puzzle.
Edit: Okay, I deliberately added a few "faux" clues to my original post in case some people undercounted. A couple common undercounts were 84 and 88. For 84, the misleading hint was "error. Well" hinting at 1984. For 88, there were a couple hints to "key" and "chord" that should make one think of a piano. But the real answer is 96 which was hinted to by this clue: "...get a semicircle. Take the measure in radians (which is pi) extended by the measure in degrees (which is 180°) and you should have the answer..." Now if you take pi and write out the digits 3.141592653589793238... you'll find '96' starting at position 180. You can confirm this by typing '96' into the Pi Search page
A: 96 triangles as enumurated in the following Count the Triangles Solution (PDF)