This is a simple but fun two-piece plaything that you can 3D print. It allows you to put a square peg in a round hole. And in a triangular one. I saw it on an episode of QI (series H, episode 1) and thought "hey, that's cool, I should make that" then forgot about it for years. You could make it with conventional tools but it is not trivial to cut perfect square or triangular holes in things nor to safely and precisely cut funny-shaped small objects.
Step 1: Design
I always like to use the simplest tool that will do the job, and in this case it was pretty clear that Tinkercad would be ideal. I made the cylinder into a wedge by drawing a cylinder 30 mm in diameter and 30 mm high, then added 30×30×15 mm wedge-shaped holes on either side. I then drew a square prism, a cylinder and a rotated roof of the matching dimensions of each side, and placed them in a row. I followed that up with a flattish oval cylinder big enough to safely encompass the 3 shapes (43×127 mm), then turned the shapes into holes.
Step 2: Print
I exported it as an .STL file and printed it on a Makerbot Replicator. I think it looks more interesting if you print the two pieces in different colors, but it hardly matters. I print them together then mix-and-match prints of different colors.
If there is any binding preventing a perfect fit, shave or sand off the offending pieces. The file below generates a pretty tight fit, so if you want it to be looser, scale down the wedge a percent or two.
The file is attached below, if you'd like to print it yourself.
Step 3: Play
It's enjoyable to watch people figure it out; it's slightly more thinky than the block toy. It's a good inexpensive stocking-stuffer for kids.
Post a picture of your print (or make it conventionally!) and I'll send you a 3 month pro membership.