putnam-v1 / putnam-1967-b4

putnam-1967-b4

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1967-b4

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-1967-b4.lean

import Mathlib

open Nat Topology Filter

theorem putnam_1967_b4 (n : ℕ)
(lockers : ℕ → Set.Icc 1 n → Bool)
(npos : n ≥ 1)
(hlockers0 : ∀ i : Set.Icc 1 n, lockers 0 i = false)
(hlockersk : ∀ k ∈ Set.Icc 1 n, ∀ i : Set.Icc 1 n, lockers k i = if k ∣ i then !(lockers (k - 1) i) else (lockers (k - 1) i))
: ∀ i : Set.Icc 1 n, lockers n i ↔ (∃ j : ℤ, j ^ 2 = i) := by
  sorry

Runs (0)

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