Question

The number of ways of selecting two squares on chessboard such that they have a side in common is
A. 225
B. 112
C. 56
D. 68

Answer 1

Hint: Here, we will first start with drawing a diagram of chess-board and find the total number of rows in a chess board and then make pairs of two consecutive rows to find the number of ways of selecting two squares on the chessboard such that they have a side in common.

Complete step by step answer
Let us examine the figure of the chessboard given below.



Now consider the first and the second row of the chessboard in the diagram above.

In the first and second row, we have 14 ways to select two squares that have only one common side.

Similarly for the second and third row, we have 14 ways to select the squares.

Since there are only 8 rows, so we can pick 8 such pairs of rows in a chessboard.

Now we will find the number of ways of selecting two squares in a chess board that have only one common side.
\[14 \times 7 = 112\]
Thus, there are 112 numbers of ways to select such squares.
Hence, the option B is correct.
Note: In this question, we have to examine the chessboard carefully.
We know that the chessboard is symmetrical in shape. So if the number of two squares having one side common in two consecutive rows is 14 then we just have to calculate the number of consecutive rows than can be taken.