Tic-Tac-Toe in Linear Algebra. Can tic tac toe be completed (5 1s and 4 0s) so that rank(A)=2, but neither side passed up a winning move? This is question 39 of an Exercise in Gilbert Strang's text on Linear algebra. Cheers.

Note that every tic tac toe game that ends in a tie with $5$ $1$s and $4$ $0$s can have its rows/columns permuted to bring it into the form $$ \pmatrix{1&1&0\\\0&0&1\\\1&0&1} $$ Note that permuting rows and columns does _not_ change the rank of a matrix.