Question 166
A chessboard has its rows and columns numbered as in the following figure. In each square, the number written is the sum of the numbers of the row and the column of that square. For example, in the square in row 4 and column 5 the number written is $4+5=9$.
a) What is the sum of the numbers written in all the squares of the board?
b) Let $S_{\text{black}}$ be the sum of all the numbers written in the black squares and $S_{\text{white}}$ the sum of all the numbers written in the white squares. What is the value of the difference $S_{\text{black}}-S_{\text{white}}$?
c) What is the value of $S_{\text{black}}$?
a) What is the sum of the numbers written in all the squares of the board?
b) Let $S_{\text{black}}$ be the sum of all the numbers written in the black squares and $S_{\text{white}}$ the sum of all the numbers written in the white squares. What is the value of the difference $S_{\text{black}}-S_{\text{white}}$?
c) What is the value of $S_{\text{black}}$?