putnam-v1 / putnam-1968-a4

putnam-1968-a4

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1968-a4

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-1968-a4.lean

import Mathlib

open Finset

theorem putnam_1968_a4 (n : ℕ)
(S : Fin n → (EuclideanSpace ℝ (Fin 3)))
(hS : ∀ i : Fin n, dist 0 (S i) = 1)
: ∑ i : Fin n, ∑ j : Fin n, (if i < j then (dist (S i) (S j))^2 else (0 : ℝ)) ≤ n^2 := by
  sorry

Runs (0)

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