Project Euler 85: Investigating the number of rectangles in a rectangular grid

Number of Rectangles in a Grid

Given a grid of size m x n, calculate the total number of rectangles contained in this rectangle. All integer sizes and positions are counted.

Examples:

numberOfRectangles(3, 2) == 18
numberOfRectangles(4, 4) == 100

Here is how the 3x2 grid works (Thanks to GiacomoSorbi for the idea):

1 rectangle of size 3x2:

[][][]
[][][]

2 rectangles of size 3x1:

[][][]

4 rectangles of size 2x1:

[][]

2 rectangles of size 2x2

[][]
[][]

3 rectangles of size 1x2:

[]
[]

6 rectangles of size 1x1:

[]

As you can see (1 + 2 + 4 + 2 + 3 + 6) = 18, and is the solution for the 3x2 grid.

There is a very simple solution to this!

public class Grid {
public static int NumberOfRectangles(int m, int n) {
// Your code here!
int sum = ;
for (int i = ; i <= m; i++)
{
for (int j = ; j <= n; j++)
{
sum += (m - i + ) * (n - j + );
}
}
return sum;
}
}

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