155

Part of 1971 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 155 All Soviet Union MO 1971 black unit squares in an inifinite board

Source:

N

unit squares on the infinite sheet of cross-lined paper are painted with black colour. Prove that you can cut out the finite number of square pieces and satisfy two conditions all the black squares are contained in those pieces the area of black squares is not less than

1/5

and not greater than

4/5

of every piece area.

combinatoricscombinatorial geometryunit squareinfinite board