Rectangles in cross-hatched grids (noch nicht übersetzt)
Problem 147
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?