This is a trick question because it is possible for someone to get confused and immediately calculate the total number of squares in a chessboard with eight rows and eight columns by using the formula (number of rows X number of columns)
= 8 X 8 = 64.
Let’s start by reducing the complexity of the situation.
The total number of 1X1 squares is presented in eight rows by eight columns on the chess board.
= 8 X 8 =64.
However, if you start thinking about 2X2 squares, 3X3 squares, and so on up to 8X8 squares, you can figure out how to answer the question.
The total number of 2X2 squares is presented in seven rows by seven columns on the chess board.
= 7 X 7 =49.
The total number of 3X3 squares is presented in six rows by six columns on the chess board.
= 6 X 6 =36.
The total number of 4X4 squares is presented in five rows by five columns on the chess board.
= 5 X 5 =25.
The total number of 5X5 squares is presented in four rows by four columns on the chess board.
= 4 X 4 = 16.
The total number of 6X6 squares is presented in three rows by three columns on the chess board.
= 3 X 3 = 9.
The total number of 7X7 squares is presented in two rows by two columns on the chess board.
= 2 X 2 = 4.
The total number of 8X8 squares is presented in one row by one column on the chess board.
= 1 X 1 = 1.
Therefore, the total number of squares presented on the chess board is found by summing up all the values obtained by 1X1, 2X2, 3X3, 4X4, 5X5,6X6,7X7 and 8X8 squares.
i.e., 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204.
Therefore, the total number of squares on the chess board is 204.
