Proofs of Existence and Optimality · Constructive Proofs of Existence

Lesson 10

Nikolai Chukhin · Alexander S. Kulikov

Problem. Is it possible to place eight non-attacking queens on a chessboard? How about fifteen bishops? Or thirty-two knights?

The diagram below shows how these pieces move: the queen moves any number of cells vertically, horizontally, or diagonally; the knight moves in an L-shape; the bishop moves any number of cells diagonally.

Mark all correct statements.

5 points

  1. One can place eight non-attacking queens.

  2. One can place thirty-two non-attacking knights.

  3. One can place fifteen non-attacking bishops.