Write an algorithm, or a set of instructions, that allow someone to follow them and guess a number between 1 and 100, told high, low, correct in response to the guess. Ideally you algorithm should be general so it is easy to change it to work for to 1 and 1000 (or 1 and N)

Guesser is reasonably intelligent, knows math.

You can write prose, bullet lists, outline, ... anything