Mathematics and Chess

Splendid collection of 99 puzzles, all built around the chessboard. Arithmetical and probability problems, chessboard recreations, geometrical puzzles, mathematical amusements and games, more. Many standard problems with new, interesting twists. You don't need to be a chess player, just know the rules of the game. Solutions.

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