The solution for this puzzle is incorrect. It assumes that the second rope burns at a constant rate. “Once the one rope (which is burning from both ends) finally burns out (and you know a 1/2 hour has elapsed), you also know that the other rope (which is burning from only one end) has exactly 1/2 hour left to burn.” This is not true. The puzzle itself states, “burning half of the rope is not necessarily 1/2 hour”. Thus the solution is incorrect.

Why not make them equilateral triangles? They also could not fall through.

The main advantage of round manhole covers is that you don’t have to line anything up. They will seat correctly no matter what “corner” goes in first.

The solution claims 3 possibilities, but there are 4.

1. The player has picked the door with the car. The host has shown Goat A.
2. The player has picked the door with the car. The host has shown Goat B.
3. The player originally picked the door hiding Goat A. The game host shows Goat B.
4. The player originally picked the door hiding Goat B. The game shows Goat A.

The answer is correct, but the solution is not.