putnam-v1 / putnam-1967-b2

putnam-1967-b2

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal putnam-1967-b2

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-b2.lean

import Mathlib

open Nat Topology Filter

theorem putnam_1967_b2 (p r A B C α β γ : ℝ)
(prbound : 0 ≤ p ∧ p ≤ 1 ∧ 0 ≤ r ∧ r ≤ 1)
(id1 : ∀ x y : ℝ, (p * x + (1 - p) * y) ^ 2 = A * x ^ 2 + B * x * y + C * y ^ 2)
(id2 : ∀ x y : ℝ, (p * x + (1 - p) * y) * (r * x + (1 - r) * y) = α * x ^ 2 + β * x * y + γ * y ^ 2)
: max (max A B) C ≥ 4 / 9 ∧ max (max α β) γ ≥ 4 / 9 := by
  sorry

Runs (0)

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