The first one, with the pentagram, took over a week. But lots of kids tried it. I know because I caught them doodling it in class.
The second one only took three days. It was this old chestnut:
Mr. Wolverton had a party and invited Mr. Zimmerman, Mr. Horst, and Miss Nowak. When they arrived, and because they are math teachers and they enjoy this sort of thing, Mr. Wolverton said, “Here’s a riddle. I have three daughters. The product of their ages is 72. The sum of their ages is the same as my house number. How old are my daughters?”
The guests went outside to look at the house number. When they came back in, they said, “This problem can not be solved!”
Mr. Wolverton said, “Oh! I forgot the most important clue. My youngest daughter prefers strawberry ice cream.”
And now I have this one up there, inspired by Paul Lockhart's new book.
Draw any quadrilateral.
Any old quadrilateral will do. Make it as ridiculous as you want. Make it concave or convex. Make it as wacky as you like. Make it disgustingly irregular.
Find the midpoint of each side.
Connect these four midpoints with four non-intersecting line segments, to make a new quadrilateral.
Something beautiful will happen.
What is it?
Now, explain why.
I have found that this proof is at the edge of what kids in regular Geometry can do, and it's beyond the edge for many of them. But I'm hoping some older kids might have fun revisiting Geometry. I'm hoping they don't realize they're doing a proof until it's too late. I left that word out intentionally, since it has teeth and would scare many of them off.