diff --git a/lean4/src/putnam_2022_a5.lean b/lean4/src/putnam_2022_a5.lean new file mode 100644 index 00000000..85567872 --- /dev/null +++ b/lean4/src/putnam_2022_a5.lean @@ -0,0 +1,20 @@ +import Mathlib + +noncomputable abbrev putnam_2022_a5_solution : ℕ := sorry +-- 290 + +theorem putnam_2022_a5 + (IsValidMove : Set (Fin 2022) → Set (Fin 2022) → Prop) + (IsValidMove_def : ∀ x y, IsValidMove x y ↔ + (x = y ∧ ∀ i < 2021, i ∉ x → i + 1 ∈ x) ∨ + ∃ i < 2021, i ∉ x ∧ i + 1 ∉ x ∧ y = x ∪ {i, i + 1}) + (IsValidGame : List (Set (Fin 2022)) → Prop) + (IsValidGame_def : ∀ g, IsValidGame g ↔ (∃ gt, g = ∅ :: gt) ∧ g.Chain' IsValidMove) + (ConformsToStrategy : List (Set (Fin 2022)) → (Set (Fin 2022) → Set (Fin 2022)) → Prop) + (ConformsToStrategy_def : ∀ g s, ConformsToStrategy g s ↔ + ∀ (i) (h : i + 1 < g.length), Even i → g[i + 1] = s g[i]) : + IsGreatest + {n | ∃ s, (∀ x, IsValidMove x (s x)) ∧ ∀ g, + IsValidGame g → ConformsToStrategy g s → ∃ gh x, g = gh ++ [x] → n ≤ xᶜ.ncard} + putnam_2022_a5_solution := + sorry