prime factorize numbers in my head. i used to just pick random numbers i saw around esp. at math competitions. picked up some useful mental math tricks this way
oh i also used to insist on crossing sidewalks and stuff in a checkerboard pattern wrt any lines in the ground but i think stuff like that is pretty common?
the main mental math trick is to check divisibility by repeatedly subtracting large multiples of the number. like check divisibility by 7 by repeatedly subtracting e.g. 70, 1400, 4900, etc. also the reverse, like subtracting into (or allowing negatives)