A man is standing at the bottom left corner of an \(11 \times 11\) grid of city streets. He wants to get to the top right corner of the grid while only travelling up and to the right. The man does not want to turn too often along the route, so he will only take a path such that any time he walks up or right, he walks at least two consecutive blocks in that direction. How many different paths can he take to the top right corner if he starts by walking to the right?
Details and assumptions
There are 11 city streets and hence 10 city blocks.