Prove that no matter how each cell of a 5 x 41 table is filled with a 0 or 1, one can choose 3 rows and 3 columns which intersect in 9 cells filled with identical numbers.

Prove that 41 is the lowest possible n for 5 x n table; i.e., the statement is not true for a 5 x 40 table.

Source: Colorado math contest.

(In reply to re: Example needed by Charlie)

I can see what you're saying, Charlie, but how do those rows and columns 'intersect' ? Rows 1, 15 and 29 are nowhere near each other.

Your reading is something like 'one can extract three rows from the grid which form a smaller grid three columns of which are either all zeros or all ones'; is that the intention?

Posted by broll on 2015-11-30 10:50:23