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Two squares are chosen at random on a chessboard. What is the probability that they have a side in common? I think the answer is 1/9. In a chessboard the 4 squares at corners share a side only with 2 squares. If the first square is at corner, then the other square must be from those 2. out of four one square can be chosen in 4c1 ways; hence total no. of ways = 4*2=8 the remaining 24 squares of sidemost rows share a side with 3 squares; hence total no. of ways = 24*3=72 other 36 squares share a side with 4 squares; thats y total no. of ways= 36*4=144 144 72 8=224 are the no. of ways in which 2 squares sharin a side can be selected. total no of ways of selecting 2 squares out of 64 squares are= 64c2 the required probability= 224/(64c2)= 1/9