MathDB
Formula on Grid Polygon

Source: Germany TST 2013 P2

April 14, 2020
combinatoricsgrid

Problem Statement

Given a m×nm\times n grid rectangle with m,n≥4m,n \ge 4 and a closed path PP that is not self intersecting from inner points of the grid, let AA be the number of points on PP such that PP does not turn in them and let BB be the number of squares that PP goes through two non-adjacent sides of them furthermore let CC be the number of squares with no side in PP. Prove that A=B−C+m+n−1.A=B-C+m+n-1.
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