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Lam's Problem


Given a 111×111 (0,1)-matrix, fill 11 spaces in each row in such a way that all columns also have 11 spaces filled. Furthermore, each pair of rows must have exactly one filled space in the same column. This problem is equivalent to finding a projective plane of order 10. Using a computer program, Lam et al. (1989) showed that no such arrangement exists.

Lam's problem is equivalent to finding nine orthogonal Latin squares of order 10.


See also

(0,1)-Matrix, Latin Square, Projective Plane

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References

Beezer, R. "Graeco-Latin Squares." http://buzzard.ups.edu/squares.html.Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Wellesley, MA: A K Peters, p. 4, 2003.Browne, M. W. "Is a Math Proof a Proof If No One Can Check It?" New York Times, Sec. 3, p. 1, col. 1, Dec. 20, 1988.Cipra, B. A. "Computer Search Solves an Old Math Problem." Science 242, 1507-1508, 1988.Lam, C. W. H. "The Search for a Finite Projective Plane of Order 10." Amer. Math. Monthly 98, 305-318, 1991.Lam, C. W. H. "The Search for a Finite Projective Plane of Order 10." In Organic Mathematics, Proceedings of the Workshop Held in Burnaby, BC, December 12-14, 19950821806688 (Ed. J. Borwein, P. Borwein, L. Jörgenson, and R. Corless). Providence, RI: Amer. Math. Soc., pp. 335-355, 1997. http://www.cecm.sfu.ca/organics/papers/lam/paper/html/paper.html.Lam, C. W. H.; Thiel, L.; and Swiercz, S. "The Nonexistence of Finite Projective Planes of Order 10." Canad. J. Math. 41, 1117-1123, 1989.Peterson, I. "Search Yields Math Proof No One Can Check." Science News 134, 406, Dec. 24 & 31, 1988.

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Lam's Problem

Cite this as:

Weisstein, Eric W. "Lam's Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LamsProblem.html

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