# Problem 147: Rectangles in cross-hatched grids

![graphic](img147.gif)

In a 3x2 cross-hatched grid, a total of 37 different rectangles could be
situated within that grid as indicated in the sketch. There are 5 grids
smaller than 3x2, vertical and horizontal dimensions being important,
i.e. 1x1, 2x1, 3x1, 1x2 and 2x2. If each of them is cross-hatched, the
following number of different rectangles could be situated within those
smaller grids: 1x1: 1 2x1: 4 3x1: 8 1x2: 4 2x2: 18 Adding those to the
37 of the 3x2 grid, a total of 72 different rectangles could be situated
within 3x2 and smaller grids. How many different rectangles could be
situated within 47x43 and smaller grids?