Consider the square of an $8 \times 8 $ chessboard filled with the number $1$ to $64$ as in given figure .If we choose $8$ squares with the property that is exactly one from each row and exactly one from each column , and add up the numbers in the chosen squares , show that sum obtained is always $260$ .
My work
I can just observer that it is happening but I don't know how to prove it . $$1+10+29+28+37+46+55+64$$ $$2+11+20+29+38+47+56+57$$ I know many pair like are existing but how I will show this ?