I made a captured ring puzzle. This is turned on the lathe out of a solid piece of wood. When people look at it, their first though is, how did I get the rings on there when the ends are larger than the insides of the rings. The answer is that I didn't get them on there. They were already there. I used the knives on the lathe to turn the surrounding material away, leaving the rings.
Then I made a cube in a cube. This one begs the question, how do you get the small cube inside the large cube when it won't fit through the holes. The answer is, again, you don't get it in, it was there to begin with. The trick is to take away the other material, leaving the small cube.
This one is done on the drill press. You set up a jig to make sure you are drilling in the exact same spot on all six sides of a cube. Then, using the depth stops, you take away a tiny bit of material at a time until the inside cube is just about to break away. Next, you use chisels, a knife, and sandpaper to clean up the cube on the inside and the inside edges of the outside cube.
I took this one to the house to show my kids. After they gave up on figuring it out, I explained to them how I done it. Then they wanted to know what else I could do. That sounded like a challenge to me.
This one is done exactly like the cube in a cube, only with a little more complication. You do it all the same way. However, you first do the tiny cube in the very center. After you have it complete, you cut away material to make the middle cube. While doing the middle cube, you have to be careful of where the inside cube is to make sure your bit does not come into contact with it and mess it up.
There are tons of articles and even videos on YouTube on how to make any one of these puzzles. However, if any of you have problems or can't find the information and are interested in making some, let me know and I'll see if I can find the links to some videos for you.