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Another method to solve the grasshopper problem (the International Mathematical Olympiad)

General Mathematics 2020-01-01 v2

Abstract

The 6th problem of the 50th International Mathematical Olympiad (IMO), held in Germany, 2009, is called 'the grasshopper problem'. To this problem Kos developed theory from unique viewpoints by reference of Noga Alon's combinatorial Nullstellensatz. We have tried to solve this problem by an original method inspired by a polynomial function that Kos defined, then examined for n=3, 4 and 5. For almost cases the claim of this problem follows, but there remains imperfection due to 'singularity'.

Cite

@article{arxiv.1911.01534,
  title  = {Another method to solve the grasshopper problem (the International Mathematical Olympiad)},
  author = {Yasushi Ieno},
  journal= {arXiv preprint arXiv:1911.01534},
  year   = {2020}
}

Comments

35 pages

R2 v1 2026-06-23T12:04:44.354Z