Grasshopper jumps and flies on a board
Source: Kvant Magazine No. 1 2019 M2542
March 14, 2023
combinatoricsKvant
Problem Statement
A grasshopper is in the left above corner of a square. At each step he can jump a square below or a square to the right. Also, he can also fly from a cell of the bottom row to a cell of the above row, and from a cell of the rightmost column to a cell of the leftmost column. Prove that the grasshopper has to do at leat flies in order to visit each cell of the square at least once. [I]Proposed by N. Vlasova[/I]