Be first to publish a solution in a refereed journal, or submit a short proof that Kimberling accepts as correct and complete. For solutions after 1 January 2025, Kimberling says the stated amount will be donated in the solver’s name to the Online Encyclopedia of Integer Sequences; it is not direct cash to the solver. The page lists “$50 or $100”; the applicable amount depends on whether the special or general version is resolved and should be confirmed with the sponsor.
Current post-2025 form: a donation to OEIS in the solver’s name.