Number Guessing
By asking a small number of innocent-sounding questions about an unknown number, it is possible to reconstruct the number withabsolute certainty (assuming that the questions are answered correctly). Ball and Coxeter (1987) give a number of sets ofquestions which can be used.
One of the simplest algorithms uses only three questions to determine an unknown number 
:
- 1. Triple and announce if the result
is Even or Odd. - 2. If you were told that
is Even, ask the person to reveal the number 
which is half of .If you were told that is Odd, ask the person to reveal the number which is half of 
. - 3. Ask the person to reveal the number of times
which 9 divides evenly into 
.
is then given by 
if was Even, or 
if was Odd. For 
even, 
, 
, 
, 
, so 
. For 
odd, 
, 
, 
, , so 
.Another method asks:
- 1. Multiply the number by 5.
- 2. Add 6 to the product.
- 3. Multiply the sum by 4.
- 4. Add 9 to the product.
- 5. Multiply the sum by 5 and reveal the result .
, since the above steps give 
.
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.
- T-Polyomino
- T-Puzzle
- Trace (Complex)
- Trace (Group)
- Trace (Map)
- Trace (Matrix)
- Trace (Tensor)
- Tractory
- Tractrix
- Tractrix Evolute
- Tractrix Radial Curve
- Tractroid
- Transcendental Curve
- Transcendental Equation
- Transcendental Function
- Transcendental Number
- Transcritical Bifurcation
- Transfer Function
- Convergent Sequence
- Convergent Series
- Conversion Period
- Convex
- Convex Function
- Convex Hull
- Convex Optimization Theory