Solution
Five Queens Rule the Board
Show the problem again
What is the minimum number of queens that can be placed on an ordinary 8×8 chessboard so that every square either holds a queen or is attacked by at least one queen? (Queens may attack each other, and attacks along a line are blocked by intervening pieces, which does not matter for the minimum here.) Give an integer.
Worked solution
Four queens never suffice: checking every placement of 1, 2, 3 or 4 queens on the 64 squares finds none that covers the whole board. Five do. For instance, queens on a1, a2, b6, e1 and f5 attack or occupy every square, as a direct check of the 64 squares confirms. So the minimum is **5**. (This is a different question from the eight-queens puzzle: here the queens may attack each other.)
Source: Queen domination on the chessboard is a classic problem going back to the 19th century (de Jaenisch, Rouse Ball); this formulation written for AxiomIQ.