The three ladies, the math enigma of “Le Monde” n° 57

Three invisible queens have been placed on a 5x5 chessboard. They behave as in chess, that is, they move as many squares as desired in a row, column, or diagonal. A queen is said to control a square if it is the square it is on, or if it can move to that square in a single move. In the figure opposite, each square of the chessboard is marked with the number of queens controlling it. For example, a square marked 2 is controlled by two of the three queens, but not by the third.