putnam-v1 / putnam-1964-a1

putnam-1964-a1

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1964-a1

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-1964-a1.lean

import Mathlib

theorem putnam_1964_a1 (A : Finset (EuclideanSpace ℝ (Fin 2)))
(hAcard : A.card = 6)
(dists : Set ℝ)
(hdists : dists = {d : ℝ | ∃ a b : EuclideanSpace ℝ (Fin 2), a ∈ A ∧ b ∈ A ∧ a ≠ b ∧ d = dist a b})
: (sSup dists / sInf dists ≥ Real.sqrt 3) := by
  sorry

Runs (0)

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