Offer 01€300Ingo Althöfer
Personal offerFirst solution wins; computer-assisted proofs are allowed, the sponsor excludes legal recourse, and the offer expires on 31 December 2037.
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The problem
Starting from any odd positive integer, repeatedly choose 3n+1 or 3n−1 by a fair coin and then remove every factor of 2. Prove that the process reaches 1 almost surely.
Open since2026sponsor-stated or introduction year
Last checked2026.07.27Catalog verification
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Reward offers
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Sources & reading
1 unique reference linksSponsor’s current Collatz-prize page ↗