Ulam's game

For Ulam's topological game where players alternate choosing binary digits, see binary game.

Ulam's game, or the Rényi–Ulam game, is a mathematical game similar to the popular game of twenty questions. In Ulam's game, a player attempts to guess an unnamed object or number by asking yes–no questions of another, but one of the answers given may be a lie.^[1]

Alfréd Rényi (1961) introduced the game in a 1961 paper, based on Hungary's Bar Kokhba game, but the paper was overlooked for many years.

Stanisław Ulam rediscovered the game, presenting the idea that there are a million objects and the answer to one question can be wrong, and considered the minimum number of questions required, and the strategy that should be adopted.^[2][3] Pelc gave a survey of similar games and their relation to information theory.^[4]

See also

• Knights and Knaves

References

1. "How to Play Ulam's Game" (PDF). Retrieved 13 June 2013.
2. Ulam (1976), p. 281.
3. Beluhov, Nikolai (2016). "Renyi-Ulam Games and Forbidden Substrings". arXiv:1609.07367 [math.CO].
4. Pelc (2002).

• Pelc, Andrzej (2002). "Searching games with errors—fifty years of coping with liars". Theoretical Computer Science. 270 (1): 71–109. doi:10.1016/S0304-3975(01)00303-6. ISSN 0304-3975. MR 1871067.
• Rényi, Alfréd (1961). "On a problem in information theory". Magyar Tud. Akad. Mat. Kutató Int. Közl. (in Hungarian). 6: 505–516. MR 0143666.
• Ulam, S. M. (1976). Adventures of a mathematician. Charles Scribner's sons. ISBN 978-0-520-07154-4. MR 0485098.