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Combinatorics
Date added 5 Aug 2026
Erdős problem 835 Does there exist a k > 2 k>2 k > 2 such that the k k k -sized subsets of {1,...,2k} can be coloured with
k + 1 k+1 k + 1 colours such that for every A ⊂ { 1 , … , 2 k } A\subset \{1,\ldots,2k\} A ⊂ { 1 , … , 2 k } with
∣ A ∣ = k + 1 \lvert A\rvert=k+1 ∣ A ∣ = k + 1 all
colours appear among the
-sized subsets of
?
$2,666 bounty · 1 piece from 1 person· last one 10 days ago
week of 18 Sept 2025 · nothing published week of 25 Sept 2025 · nothing published week of 2 Oct 2025 · nothing published week of 9 Oct 2025 · nothing published week of 16 Oct 2025 · nothing published week of 23 Oct 2025 · nothing published
Solve it A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
Add a piece A lemma, a definition, a special case. There is no race: when someone finishes the problem, the pool splits between everyone whose work led there.
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← Erdős problem 829 Erdős problem 849 → What has been built 1 piece · 10 lemmas
1 Sept 2026
Proof target
import FormalConjectures.ErdosProblems.«835»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos835.erdos_835" := by
sorry
end Bounty
Open this target’s Challenge.lean Original conjecture (Lean type)
(∃ k > 2, Erdos835.Property k) ↔ TrueOriginal conjecture source: FormalConjectures/ErdosProblems/835.lean
Source type SHA-256 sha256:f967e72c8bf53da5895721dfe2bcf951ec3b0ace3ff8180ca1355d1639d592a4
Task id fc-8432eac9-erdos835-erdos-835-6af7c08e86-formalized-v1
Task commitment sha256:bb6579870beda9c85b00cb710b67d4b6ded5422718cdb0ce4e8c1cdfa7079a47 week of 30 Oct 2025 · nothing published
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18 Sept 2025 a year of work on this problem 10 Sept 2026
erdosproblems.com/835
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
Our channel is in the Bittensor Discord server. Join the server first, then open the channel to send your report.
Reward
$2,666
for closing this problem
Whoever closes it takes the bounty. Published pieces that helped get there share a separate contribution pool, paid out once the problem is closed.
Set by bounty policy dynamic-age-v2-locked: the amount is worked out from how long the problem has stood open, so it moves as the pool and the pool's age profile move.
Prove it or break it
The same problem accepts both. You can submit a proof of the statement or a counterexample that refutes it, and you choose which when you submit.
Prove the statement no attempts
Find a counterexample no attempts
Erdős problem 835 · Conjectures.io