By asking a small number of innocent-sounding questions about an unknown number, it is possible to reconstruct the number with absolute certainty (assuming that the questions are answered correctly). Ball and Coxeter (1987) give a number of sets of questions which can be used.
One of the simplest algorithms uses only three questions to determine an unknown number :
Another method asks:
References
Bachet, C. G. Problèmes plaisans et délectables, 2nd ed. 1624.
Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 5-20, 1987.
Kraitchik, M. ``To Guess a Selected Number.'' §3.3 in Mathematical Recreations. New York: W. W. Norton,
pp. 58-66, 1942.