This writeup contains the solution to

Triangle Challenge. If you haven't seen that node, I suggest you start there.

**I'm ready to read the solution!**

Right, you have come here because you've cracked the Triangle Challenge, or you've simply given up. So, what's up? Well, let's just start by saying that I fooled you a bit. You have in fact not made the same triangle, but one which is slightly bigger. In fact, it's exactly 2 squares bigger; the extra space in the middle.

**How did you do that?**

Well, if you look closely at the figures, you discover that the triangle isn't really a triangle at all. (Oops, I guess I lied again, dammit!) The original "triangle" is slightly concave, which you can see by the fact that 11/8 > 4/3. In other words, the slope of the 11/8 piece is steeper than the slope of the 4/3 piece. The second "triangle" is then slightly convex. You would also see this if you cut out the pieces accurately, but not if you are just a bit sloppy.

**So what's clever about this, then?**

Well, you might say "nothing". I would disagree. I agree, the challenge was really a bit unfair, since I was lying to you in the first place. But you should have been able to see that, so what are you whining about? :)

What I find brilliant about this, is how the extra space makes up exactly two squares in the middle. It's actually quite well made (did I tell you I didn't make it?). I hope you had as much fun pondering it as I had.