Five Queens Rule the Board
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.
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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.