Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :

Step-by-step solution

Total ways of choosing 2 squares = C 2 64 = 32 × 63 Now, each corners has two neighbours, and each 24 squares across the outer edge of the chess board has 3 neighbours, and remaining 36 squares have four neighbours Favorable ways = 1 2 4 ( 2 ) + 24 ( 3 ) + 36 ( 4 ) = 1 2 224 = 112 . Since, every pair counted twice. Required probability = 112 32 × 63 = 1 18