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11.6

Part of 1998 All-Russian Olympiad Regional Round

Problems(1)

A-B = 4(a -b) bw cells - All-Russian MO 1998 Regional (R4) 11.6

Source:

9/17/2024
A polygon with sides running along the sides of the squares was cut out of an endless chessboard. A segment of the perimeter of a polygon is called black if the polygon adjacent to it from the inside is which cell is black, respectively white if the cell is white. Let AA be the number of black segments on the perimeter, and BB be the number of white ones, Let the polygon consist of aa black and bb white cells. Prove that A−B=4(a−b)A-B = 4(a -b).
geometryperimeter