(1) Will you guys want a concise (as short as possible) but logically valid solution, or it should include some "heuristics", meaning that the solution writer would express "why" or "how" to think of a method?

(2) Will you guys want more mathematical symbols or more words?

(3) Are multiple solutions favored, or you would like to have a single most effective solution?

(4--) Your thoughts :-)

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## Comments

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TopNewestI like using words to explain the mathematical steps. It's ideal if I can supplement the mathematical rigor with intuition. This does seems to be lacking in textbooks, but sometimes I wonder if writers favor conciseness simply in order to cut printing costs... I also like having as many solutions as possible. Sometimes it's fun to see how many ways you can approach a problem.

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I'd say Putnam loves compact solutions. For some queer reason they respect huge integrals and summations when you can put the same thing in words very easily. They look for rigor so they would prefer an epsilon-delta proof(which is disgusting thing for me, personally) rather than an answer like "f(x) grows exponentially and g(x) grows almost linearly,so f(x)>g(x) at least in this interval"

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There's an old joke in theoretical physics "Never calculate something until you already know the answer." In essence, this means that it's rare to be able to blindly slog through algebra and prove something new without having the gist first about where you're trying to go and what you should get. However, this gist is usually derived entirely with words or pictures or other physical arguments, not math. The ability to logically reason and create based on principles is the rarest gift, even among 'professionals'. One of my goals at Brilliant is to provide problems where students can practice that ability, and so I like solutions that show the creative steps in words which are then supplemented with mathematical rigor. Just math doesn't do it for me.

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I totally agree. Indeed, is there a way to insert pictures when I am writing a solution?

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Heuristics are good. Solutions are meant to explain to others not only what you did, but why you chose the steps you did. The why is after all what transfers to other problems. The exact steps, not so much.

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HOW I can strong my differential equation

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