Are there papers/texts on "tricks" to mathematical thinking? More details inside.

This might be a bit vague but here it goes...

Some examples to set the stage:

Example 1) Based on the game 24

Q: Try and create the number 24 using standard arithmetic rules and all of following integers once; 1, 3, 4, 6

A: 6 / (1 - 3/4)

Example 2) A question based on a problem projecteuler.net

Q: Starting from the top-left corner of a n x n grid, without backtracking, how many ways can you take to get to the bottom-right corner

A: (2n!)/(n!*n!) or 2n Choose n

The first example is a bit trivial. If you had tried to solve it yourself it might take you a while to structure the arithmetic to get the right answer but once you know this type of "trick" then you can solve other "difficult" ones such as 1, 3, 7, 8.

The second example might have more scope. The question on projecteuler was stated as a 20x20 grid to solve. One can brute force the solution using recursion and a spread sheet reasonably easily but if you take the combinatorial approach there are 2n turns to make and n of them have to be right turns, you can get the solution easily. This "trick" of thinking can be applied to other problems such as how many ways can you divide a chessboard up into rectangles.

My question is are there texts/papers on these different "tricks" of mathematical thinking in order to reduce problems into something easier to solve, much like switching to polar co-ordinates when given a stubborn integral?

Hope this is clear enough to get a good response.