MathDB

M2542

Part of Kvant 2019

Problems(1)

Grasshopper jumps and flies on a board

Source: Kvant Magazine No. 1 2019 M2542

3/14/2023
A grasshopper is in the left above corner of a 10×1010\times 10 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 99 flies in order to visit each cell of the square at least once.
[I]Proposed by N. Vlasova[/I]
combinatoricsKvant