putnam-v1 / putnam-1965-b5

putnam-1965-b5

proved

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1965-b5

What it runs

The Lean statement the swarm must prove — kernel-verified at Gate A. The trailing sorry is the open obligation a proof replaces.

goals/putnam-1965-b5.lean

import Mathlib

open EuclideanGeometry Topology Filter Complex SimpleGraph.Walk

theorem putnam_1965_b5 {K : Type*}
[Fintype K]
(V E : ℕ)
(hV : V = Nat.card K)
(hE: 4*E ≤ V^2)
: ∃ G : SimpleGraph K, G.edgeSet.ncard = E ∧ ∀ a : K, ∀ w : G.Walk a a, w.length ≠ 3 := by
  sorry

Runs (0)

No runs recorded for this suite yet — they appear here as the swarm attempts the benchmarks.