Table of Contents

Arithmetic and Probability Problems Number of rectangles Result of the chess game Number of chess players in the tournament Sum of the crossed-out numbers Four selected numbers Nonattacking rooks and the sum of numbers Nonattacking rooks and the value of a determinant Rook polynomials Encircling points on a square Probability of attacking queens Probability of king's tour Match between two chess players Two consecutive wins Intersection of square's edges Solutions Chessboard Diversions Symmetry in the ending Retrograde problem The immovable king No-three-in-line problem Four-in-a-row problem Minimum-pieces problems Four attacking queens Minimum and maximum attacks Minimum and maximum moves The eight-queens problem Winning a game with the minimal length of moves Replacement problem with queens Walk through a chess park Beetle's tour on a chessboard Traveling salesman's route Five rooks Police patrol Four moving beetles Arrangement of numbers Sinking the ships Knight's fourfold attacks Kriegsspiel problem Mate with eight rooks Mate by two queens Check by two knights Minimal game to kings Mirror-image selfmate Solutions Chess-piece Tours The queen's shortest route Five moves of the queen King's magic re-entrant path The longest uncrossed knight's tour Knight's re-entrant path Roundabout knight's tour Knight's tour on a 4x4 board Knight's tour on a quarter of chessboard Knight's re-entrant path over the cube Knight's tour on the three-dimensional 4x4x4 board Knight's tour on an infinite board The largest bishop's tour The longest and the shortest king's tours Lost-king tour Rook's re-entrant path with obstacles Rook's dance around pawns The number of knight's paths Guarini's problem Variant I of Guarini's problem Variant II of Guarini's problem Knights crossing over the Danube Knight on a solitaire board Camel's tour Solutions Geometric puzzles Maximum number of cut squares The first joiner's problem The second joiner's problem The third joiner's problem Geometrical paradox: 64 = 65 Four pawns on the edges of a chessboard Dividing a chessboard with four knights Assembling a chessboard Rooks and knights on a 6x6 board Dividing by matches Chess cube Building a 6x6x6 cube Piece-placement problem Figure of the smallest diameter Where is the king? Solutions Mathematical Amusements and Games Covering by dominoes Another problem with covering dominoes Covering by k-minoes Pentaminoes on a chessboard Rolling cube on a chessboard Rolling cubes on a 3x3 board Presidential candidates Switching puzzle on a chessboard Mosaic transfiguration The pushing rook King-cornering game Domino game on a chessboard Solutions Miscellaneous Puzzles Suicidal king Nonattacking superqueens Elimination of squares Termite on a cube Movement of nine queens Magic squares on a chessboard Magic cube Extension of the magic squares Magic domino squares Latin squares Shinkman's zig-zag problems Pistol theme Cylindrical chess The eight-queens problem on a cylindrical board Toroidal chess Projective chess Combined problems Coloring a 9x9 square Coloring a chessboard Solutions