Given a (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.
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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." Science242, 1507-1508, 1988.Lam,
C. W. H. "The Search for a Finite Projective Plane of Order 10."
Amer. Math. Monthly98, 305-318, 1991.Lam, C. W. H.
"The Search for a Finite Projective Plane of Order 10." In Organic Mathematics,
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(Ed. J. Borwein, P. Borwein, L. Jörgenson, and R. Corless).
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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,
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(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.
