You are in a maze of twisty little passages, all alike...

One hot summer, a math professor led a couple of his students down into the Badlands and proclaimed "I'm going to find an optimal path to the other side."

Somewhat skeptical, the students followed. After wandering about for about 15 hours in the hot sun, the professor started ranting uncontrollably about weak paths, strong paths, weakly strong paths, strongly weak paths, and how strongly weak paths were in fact stronger than weakly strong paths, but neither was obviously as strong as a strong path. However, even as strong as a strong path was, it was not as strong as a super-strong path.

One some point, one of the students remarked, "what the fuck is he talking about? Did I miss a lecture?"

At that point, the professor then suddenly dropped dead. After a few moments of silence, the students merely shrugged and started to walk back to the highway.

"Wait a second," exclaimed Mike. "I think I'm going to go take his cardigan sweater----I might need it later."

"Ok, now let's go find some ice water."

Corollary 1: A real math professor would have simply proven the existence of an optimal path and left finding it as an exercise.

Corollary 2: One should be extremely wary of math professors wandering around in the wild.

Exercise 1: Prove that the color of the sweater is maroon.