Question: There are rectangles in a 3 7 array. Show that any 2 - coloring of the 2 1 points will result in at least one

There are
rectangles in a 37 array. Show that any 2-coloring of the 21 points will result in at
least one of them having 4 vertices of the same color.
Can such monochromatic rectangles be avoided in a 2-coloring of a 217 array?
Can monochromatic rectangles be avoided in a 54 array?
Can monochromatic rectangles be avoided in a 55 array?
There are rectangles in a 3 7 array. Show that

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