But very hot water does freeze faster than cold water. Some of the water evaporates leaving less water to freeze. So in some roundabout, unintended way, it is an apt analogy, as the desired goal is reached by reducing the amount in the "pool". Not saying you're wrong, just that maybe you should stick with something safe like car analogies.

Name one. I bet there's some programming involved in there.

You lose. Intractability

The whole course consisted of doing proofs. The course was so theory based that the notion of using a computer just to email the professor to ask a question seemed out of place. Coincidentally, the course I took was taught by Manuel Blum (husband of Lenore Blum in the article).