Jared nicely solved [Puzzle 29](https://forum.azimuthproject.org/profile/1729/Jared%20Summers). Good use of proof by contradiction, Jared!

Anyone who isn't used to writing proofs should look at Jared's. This is how you should write proofs when you're being careful. When you get a math degree you do a thousand homework problems involving proofs. I suppose this is also true for some branches of computer science. By the end of this training, you can crank out proofs quite quickly unless they involve a deep and difficult trick. Once you're good at this, you can start slacking off a bit and write proofs that skip some steps. But anyone who hasn't gone through some training like this is likely to screw up when they skip steps!