Excel Function or VBA

Is this an absolute example or are you wanting to generalise the solution for combinations of different box sizes.

Trivially in this case of course and merely by imagining the placements you can fit two of the 24 x 24 boxes and two of the 24 x 12 boxes. Leaving 144 sq.units unused

This appears to be a fairly typical packing problem. Packing problems are fairly common in math and computer science discussions, and they are fairly difficult to program (especially if you want to program them efficiently).:

https://en.wikipedia.org/wiki/Packing_problem
http://mathworld.wolfram.com/Bin-PackingProblem.html
a link in the wikipedia page leads here: https://www.codeproject.com/Articles...gorithm-for-bu

or, if you use a different visualization for the problem -- instead of packing smaller rectangles within a larger rectangles visualize cutting smaller rectangles from a larger rectangle -- and you end up with the (2D) cutting stock problem. You may find this old discussion thread interesting: https://www.mrexcel.com/board/thread...6/#post-327860

Most of these problems reduce to the knapsack problem which is NP-hard/NP-complete -- meaning that there just are not efficient algorithms for getting a rigorous solution. Most Excel/spreadsheet based solutions that I see involve Solver. The programmer works out a way to describe the arrangement of rectangles within the larger rectangle (I don't have any specific ideas, yet for this, but the codeproject link above describes a way) then compute "waste" (or other optimization parameter). Then call Solver and tell it to optimize "waste" by changing "arrangement of rectangles". Then see what Solver comes up with.

One idea that might simplify this particular problem. Two 12x24 rectangles side by side make up one 24x24 rectangle. It might be easier to solve the problem for the 12x24 rectangles alone. Then look at that solution and recognize that any two 12x24 adjacent rectangles can be replaced with one 24x24.

It is a challenging problem -- especially if it is one that you have not tackled before. Study some of these and see if they help. Then let us know how you decide to proceed and how we can help you implement your chosen algorithm.