Problems – We Solve Problems
Filter Problems
Showing 1 to 14 of 14 entries

#### Chessboards and chess pieces , Pigeonhole principle (other)

What is the largest number of horses that can be placed on an $8\times8$ chessboard so that no horse touches more than seven of the others?

#### Chessboards and chess pieces , Examples and counterexamples. Constructive proofs , Pigeonhole principle (other)

What is the smallest number of cells that can be chosen on a $15\times15$ board so that a mouse positioned on any cell on the board touches at least two marked cells? $($The mouse also touches the cell on which it stands.$)$

#### Chessboards and chess pieces , Pigeonhole principle (other) , Proof by contradiction

On a chessboard, n white and n black rooks are arranged so that the rooks of different colours cannot capture one another. Find the greatest possible value of n.

#### Chessboards and chess pieces , Pigeonhole principle (finite number of poits, lines etc.) , Proof by contradiction

100 queens, that cannot capture each other, are placed on a $100 \times 100$ chessboard.
Prove that at least one queen is in each $50 \times 50$ corner square.

My Problem Set reset
No Problems selected