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References



7. References

Anderson, W., Matching and the game of slither, J. Comb. Theory 17(B) (1974) 234-239.

Averbach, B. and O. Chein, Mathematics: Problem Solving Through Recreational Mathematics, W.H. Freeman, San Francisco, 1980. (Republished by Dover Press.)

Beasley, J. The Mathematics of Games, Oxford U. Press, New York, 1989.

Beck, A. and D. Crowe, M. Bleicher, Excursions into Mathematics, Worth, New York, 1969. (Republished, A. K. Peters, 2000)

Berlekamp, E., and J. Conway, R. Guy, Winning Ways, Academic Press, London, 1982 (Being republished by A. K. Peters).

Bouton, C., Nim, a game with a complete mathematical solution, Annals of Mathematics 3 (1902) 35-39.

Conway, J., All games bright and beautiful, Amer. Math. Monthly 84 (1977) 417-434.

Conway, J., A gamut of game theories, Mathematics Magazine 51 (1978) 5-12.

Conway, J., On Numbers and Games, Second edition, A. K. Peters, Natick, 2000.

Conway, J. and R. Guy, The Book of Numbers, Springer-Verlag, New York, 1996.

Fraenkel, A., Recreation and depth in combinatorial games, in R. Guy and R. Woodrow, (ed.), The Lighter Side of Mathematics, Mathematical Association of America, Washington, 1994, p. 159-173.

Fraenkel, A., Combinatorial games: selected bibliography with a succinct gourmet introduction, in R. Nowakowski, (ed)., Games of No Chance, Cambridge U. Press, New York, 1996, p. 493-537.

Gale, D., Tracking the Automatic Ant, Springer-Verlag, New York, 1998.

Gardner, M., Wheels, Life and Other Mathematical Amusements, W.H. Freeman, New York, 1983. (Chapters 8, 11, 14, and 18.)

Grundy, P., Mathematics and games, Eureka 2 (1939) 6-8 (reprinted in Eureka 27 (1964) 9-11.

Guy, R. Fair Game, COMAP, Arlington, 1989.

Guy, R. Combinatorial Games, in Handbook of Combinatorics, R. Graham, and M. Grotschel, and L. Lovasz, (eds.), Vol. II, North-Holland, Amsterdam, 1996, p. 2117-2162.

Guy, R., (ed.), Combinatorial Games, Volume 43, Proceedings of Symposia in Applied Mathematics, American Mathematical Society, Providence, 1991.

Guy, R. and R. Woodrow, (ed.), The Lighter Side of Mathematics, Mathematical Association of America, Washington, 1994.

Harary, F., Achievement and avoidance games for graphs, Ann. Discrete Math. 13 (1982) 111-120.

Harary, F. and K. Plochinski, On degree achievement and avoidance games for graphs, Mathematics Magazine 60 (1987) 316-321.

Knuth, D., Surreal numbers, Addison-Wesley, Reading, 1974.

Nowakowski, R., (ed.), Games of No Chance, Cambridge U. Press, New York, 1996.

Nowakowski, R., (ed.), More Games of No Chance, Cambridge U. Press, New York, 2003.

Propp, J., A new take-away game, in R. Guy and R. Woodrow, (ed.), The Lighter Side of Mathematics, Mathematical Association of America, Washington, 1994, p. 212- 221.

Sibert, W. and J. Conway, Mathematical kayles, Internat. J. Game Theory, 20 (1992) 237-246.

Silverman, D., Your Move, McGraw Hill, New York, 1971.

Sprague, R, Über mathematische Kampfspiele, Tôhoku Math. J., 41 (1935-1936) 438-444.

Note 1: Many examples of combinatorial games can be found in the books and articles of Martin Gardner.

Note 2: Those who can access JSTOR can find some of the papers mentioned above there.

 


  1. Introduction
  2. What is a combinatorial game?
  3. Finding the winner of a game
  4. Solving Nim
  5. Towards a theory for combinatorial games
  6. Towards the surreal
  7. References

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