Blind Dates

stover calendar trick

A calendar curiosity by Canadian magician Mel Stover:

Offer any month’s calendar to a friend and have him outline a 4×4 square of dates. Ask him to circle any date in that square and cross out the other numbers in its row and column. Have him do this three more times and then add the circled numbers.

You can predict his answer by totaling the numbers in either pair of diagonally opposite corners in the square and doubling that number. Why does this work?