I take a pair of 10x10 chessboards. Initially I overlay them exactly on top of one another and find the point 4 squares along and 2 squares down and drive a nail through both boards. The I rotate the top board around the nail until the bottom left corner of the upper board coincides with the bottom edge of the lower board.

I take a second pair of 10x10 chessboards and do exactly the same except that this time the nail is driven through at a point 3 squares along and 1 square down.

The question is: in which scenario is the area of overlap between the upper and lower chessboards greatest?