Althöfer · Optimal-play 3n±1 game

Prove that every odd starting value reaches 1 in the sponsor’s adversarial 3n±1 game under optimal play, or give a counterexample.

Collatz variantsinteger iterationdiscrete dynamics

The problem

Prove that every odd starting value reaches 1 in the sponsor’s adversarial 3n±1 game under optimal play, or give a counterexample.

Open since2023sponsor-stated or introduction year

Last checked2026.07.27Catalog verification

Offer 01€500Ingo Althöfer

Personal offer

First solution wins; computer-assisted proofs are allowed, the sponsor excludes legal recourse, and the offer expires on 31 December 2037.

Published deadline: 2037-12-31