putnam-v1 / putnam-1968-a3

putnam-1968-a3

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1968-a3

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-a3.lean

import Mathlib

open Finset symmDiff

theorem putnam_1968_a3 (α : Type*) [Finite α] :
    ∃ (n : ℕ) (s : Fin (2 ^ n) → Set α),
      s 0 = ∅ ∧
      (∀ t, ∃! i, s i = t) ∧
      (∀ i, i.1 + 1 < 2 ^ n → (s i ∆ s (i + 1)).ncard = 1) := by
  sorry

Runs (0)

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