Proofs of Existence and Optimality · Non-constructive Proofs of Existence

Lesson 4

Nikolai Chukhin · Alexander S. Kulikov

Problem. Mark all correct statements.

5 points

  1. Among any five hundred people, there are two born on the same day of the year.

  2. Among any 101 integers, there are two whose difference is divisible by 100.

  3. If 1001 balls are placed into 20 boxes, then at least one box contains at least 51 balls.

  4. If 1000 balls are placed into 20 boxes, then at least one box contains at least 51 balls.