Other correct solutions were sent in by Scott Baker, Stepahnie Aneloski. Further solutions were submitted by alumnus Kevin Bourillion, and from Lenny Gibson and his AEGIS Math Squad, Burkart Venzke, Philippe Fondanaiche, Vadim Ponomarenko, Mike Lynch, Ivan Lisac, Lou Cairoli, Jan Siwanowicz, Jeff Anderson, Paul Buskell.

Here is Jan Siwanowicz's solution.  In the seven rows, at least four of the rows will have a majority of one of the colors, call it C; so C appears at least twice in each of those rows.  But that means that at least one of the the combinations "C appears in columns 1 and 2",  "C appears in columns 1 and 3", "C appears in columns 2 and 3" must appear in two of the rows, thereby forming a rectangle.

Professor Ponomarenko suggests taking this week's problem as the basis of the following game:  Two players take turns placing differently coloured counters on a 3 by 7 lattice.  The first to form a rectangle of her/his colour wins.  With the result of this week's problem, we know there will always be a winner!  Of course, the game gets more interesting if lattices of different sizes are used.  He suggest using a 6 by 6 board and allowing rectangles in any orientation -- even diagonal.  

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