Brain Game: Draw Two Lines, Win a T-shirt!


Last night, I couldn't sleep. And what does a geek do when he can't sleep? He creates math puzzles in his head, that's what. For some reason, when I closed my eyes, I visualized a square. Then I began splitting up the square using straight lines and taking note of the resultant shapes. (No, I'm not on drugs. And yes, it helped me sleep, thank you for asking.) When I woke up, I jotted down what I remembered, and a little tweaking created today's Brain Game.

If you're not a math geek, hang on. It could get bumpy. And you'll probably want to look at the image to follow along. Click to go on. >>

I noted that by using two traversing lines, you could create three triangles (for 9 sides total), two triangles and a quadrilateral (for 10 sides), one triangle and two quadrilaterals (for 11 sides), and so on all the way to 16. But there was one exception: the one that would result in shapes with a total of 13 sides.

square2.gif /

Is there an answer? I'm not certain. I might be overlooking something obvious. Of course, our site doesn't have the ability to attach files to comments. But if you DO think you have an answer, sketch it out to a GIF or JPG file, then send it to and we'll take a look at it. If you're the first to successfully solve the problem, I'll send you the mental_floss T-shirt of your choice.

And if no one can figure it out, then I henceforth decree that this puzzle shall now and forever be known as Sandy's Paradox, and I officially throw my hat into the ring for a Fields Medal. Woohoo!