Problem #PRU-66114

Problems Methods Colouring Colouring (other) Examples and counterexamples Pigeonhole principle Pigeonhole principle (other)

Problem

A grasshopper can make jumps of 8, 9 and 10 cells in any direction on a strip of \(n\) cells. We will call the natural number \(n\) jumpable if the grasshopper can, starting from some cell, bypass the entire strip, having visited each cell exactly once. Find at least one \(n > 50\) that is not jumpable.