A Piece of the Pi: mathematics explained

A Piece of the Pi: mathematics explained

Arranging queens on a chessboard

Richard Green's avatar
Richard Green
May 05, 2024
∙ Paid

What is the minimum number of chess pieces of a given type needed to attack every vacant square of the board? The answer turns out to be 9 for kings, 5 for queens, 8 for bishops or rooks, and 12 for knights. The picture above shows some minimal solutions to the problem for kings, queens, bishops, and knights, and the placement shown for the bishops also…

Keep reading with a 7-day free trial

Subscribe to A Piece of the Pi: mathematics explained to keep reading this post and get 7 days of free access to the full post archives.

Already a paid subscriber? Sign in
© 2025 A Piece of the Pi
Privacy ∙ Terms ∙ Collection notice
Start your SubstackGet the app
Substack is the home for great culture