A rectangular array has n rows and 6 columns, where n≥2. In each cell there is written either 0 or 1. All rows in the array are different from each other. For each two rows (x1,x2,x3,x4,x5,x6) and (y1,y2,y3,y4,y5,y6), the row (x1y1,x2y2,x3y3,x4y4,x5y5,x6y6) can be found in the array as well. Prove that there is a column in which at least half of the entries are zeros. vectorfloor functioncombinatorics proposedcombinatoricsBaltic Way2005#7