Susan made a 4x4 grid of squares, being a 5x5 grid of horizontal and vertical lines. If you figure it out, you can see there are 100 rectangles that can be made out from portions of those vertical and horizontal lines.

Susan then made a much larger such square grid. The number of little squares in it was a 3-digit number. She calculated how many rectangles of all sizes and shapes were thus formed on that new grid. She then cut along one of the straight lines of the grid to make two rectangular grids. Then she calculated the total number of rectangles in each of the two new pieces. It turned out that the total of these two numbers was exactly two thirds of the number visible on the original large square grid from which the two were cut.

What was the size of the original large grid before she cut it, and how far away from an edge did she cut it?

Bonus:

Are there any smaller grids for which this is possible?

 gives three possibilities for smaller squares: 1+1=2, 1+2=3, 2+6=8

Posted by K Sengupta on 2023-06-26 07:45:17