The most useful trick I've used is writing out numbers or calculations algebraically (in my head). For instance, if you're squaring a number near some round num

The most useful trick I've used is writing out numbers or calculations algebraically (in my head). For instance, if you're squaring a number near some round number, say 52, one can write. (52)^2 = (50 + 2)^2 = 50^2 + 2 * 50 * 2 + 2^2 = 2500 + 100 * 2 + 4 = 2704. Also really helpful: you can do powers by memorizing a few precomputed logarithms, knowing extrapolation and knowing how to convert bases. My favorite method for doing logarithms tends to be a mix between a 'guess and check' Newton's method, and Feynman's algorithm: Consider the problem of finding the logarithm of a fractional number between 1.0 and 2.0 (the algorithm can be generalized without too much difficulty). Feynman observed that any such number can be uniquely represented as a product of numbers of the form 1 + 2^-k, where k is an integer. Testing each of these factors in a binary number representation is simply a matter of a shift and a subtraction. Once the factors are determined, the logarithm can be computed by adding together the precomputed logarithms of the factors. The algorithm fit especially well on the Connection Machine, since the small table of the logarithms of 1 + 2^-k could be shared by all the processors. The entire computation took less time than division. http://www.longnow.org/views/essays/articles/ArtFeynman.php http://www.longnow.org/views/essays/articles/ArtFeynman.php