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2018 pieces by cutting 2017 times a square, numbers 0,1,2 (HOMC 2017 S Q9)

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September 8, 2019
combinatoricscombinatorial geometry

Problem Statement

Cut off a square carton by a straight line into two pieces, then cut one of two pieces into two small pieces by a straight line, ect. By cutting 20172017 times we obtain 20182018 pieces. We write number 22 in every triangle, number 1 in every quadrilateral, and 00 in the polygons. Is the sum of all inserted numbers always greater than 20172017?
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