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There's no substitute for a good mathematical intuition, especially as you tackle the more difficult problems. But having a standard bag of tricks up your sleeve can be very helpful. Just use them as a tool, not as a crutch.

If you're interesting in this sort of thing, I highly recommend working your way through the Art of Problem Solving texts (www.artofproblemsolving.com).

Seems like the kind of thing that would be more fun to write than to read...
It took me more than one try to parse the meaning from that title.
Just to point out a typo: it's "Terence Tao", not "Terrence Tao".
I can't edit that anymore, but thank you!
Most of the higher level math text books I've read present theorems and their proofs , but not much on strategies for actually solving problems (a notable exception: Wilf's Generatingfunctionology), so this seems like it should become a very nice resource.

As one would expect from a brand new site, it's rather short on content. The content that's there right now, though is pretty good.