## The evolution of a solution

As a TA, I sometimes TA for a course whose coursework has no ready solutions. Then the following happens.

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Iteration 0: No solution. These problems are impossible. The lecturer is a sadist. These are his research problems.

Iteration 1: Death is the only solution.

Iteration 2: Hey, if we know “A” this problem is easily solved. Hooray!

Iteration 3: Oh, “A” follows from this problem. Dang.

Iteration 4: If we assume “B” is known, this is both easy and elegant!

Iteration 5: If we assume “B”, we’re assuming something not known or proven on this course!

Iteration 6: It’s one page if I hand-wave the hard part!

Iteration 7: It’s three pages and no hand-waving!

Iteration 8: It’s three pages, no hand-waving, and assuming $1 < 0$ holds!

Iteration 9: Hang on a minute, this is not a problem about “X”. That’s why no “X”-literature had a peep of it.

Iteration 10: This is about “Y”! And it’s an easy “Y”-problem!

Iteration 11: Three lines, easy peasy… aw crap, that inequality’s not strict.

Iteration 12: Three lines, plus eleven special cases, can this really be— (phone rings)

Iteration 13: “Misprint, Mr. Lecturer? The one in Problem 3, right? Right right. What? I meant the inequality… oh, that’s a different misprint?”

Iteration 14: It’s not an “Y”-problem. It’s an “X”-problem, and the zero was clever misdirection for infinity.

Iteration 15: I have… a solution? A skeleton anyway; let’s throw some meat on this pony!

Iteration 16: It’s a elephant. I can’t give this solution to the little ones. First thing, my wrist would break at the blackboard.

Iteration 17: I could use transparencies… Wait, no, I’d better try simplifying this. Get some jumping jacks, elephant solution!

Iteration 18: Right, I don’t need the special case where $r>1$ and $r<-1$; silly me.

Iteration 19, the homework meeting: “Mmh, yeah. You can prove it that way too.” (crushes paper, cries a silent tear, moves to the next problem)

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Iteration 19 can be averted by having a handout. (“Yeah, I guess you could use the obvious, elegant solution Mr. Poopypants put on the blackboard. If on the other hand you want a solution with pizazz and loxodromic Möbius transformations… well, one out of two ain’t too bad… here’s a handout… Aw, come on people, don’t you have saunas to set fire to or something?”)