Problem #PRU-66114

Problems Methods Colouring Colouring (other) Examples and counterexamples. Constructive proofs 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.