025: Lam's Problem

Proposed by Toby Walsh

Consider a 111 by 111 binary matrix. The goal is to put 11 zeros in each row in such a way that each column has 11 zeros, and each pair of rows must have exactly one zero in the same column.

This problem is equivalent to finding a projective plane of order 10. It is also equivalent to the <111,111,11,11,1> BIBD problem Balanced Incomplete Block Designs.