## Compfiles: Catalog Of Math Problems Formalized In Lean

## Imo1972P1

```
import Mathlib.Tactic
/-!
# International Mathematical Olympiad 1972, Problem 1
Prove that from a set of ten distinct two-digit numbers (in
decimal), it is possible to select two disjoint subsets whose
members have the same sum.
-/
namespace Imo1972P1
theorem imo1972_p1 (S : Finset ℕ)
(Scard : S.card = 10)
(Sdigits : ∀ n ∈ S, (Nat.digits 10 n).length = 2) :
∃ S1 S2 : Finset ℕ, S1 ⊆ S ∧ S2 ⊆ S ∧
Disjoint S1 S2 ∧ ∑ n ∈ S1, n = ∑ n ∈ S2, n := sorry
end Imo1972P1
```

File author(s): David Renshaw

This problem has a complete formalized solution.

Open with the in-brower editor at live.lean-lang.org: