The spreadsheet for this problem needs to have quite a lot of rows, trying out numbers of beads going from 1, 2, 3, . . . to maybe 500.
This makes very large file sizes, which could take a long time to download.
So I have kept the files as small as possible, still containing the important formula for each process, but leaving you to extend the formula to a more useful number of rows.
Small File More Beads is the smallest file. A11 to M11 need to be replicated (highlight across and as far down as you want to go then Fill Down from the Edit menu)
More Beads 1 is larger, around 200 rows (beads), but at least shows some solutions.
More Beads 2 is the same as More Beads 1 but the commission can be adjusted from 0 upwards.
Excel will just crunch away at the calculation because I told it to, but I know it is the non-fraction results that are the real solutions to my problem. Remember the beads are not broken into fractions according to the puzzle. I just need to look for the rows that don't have decimal (fraction) values.
I've also used an Excel trick to help me, called Conditional Formatting. It makes the results which matter stand out. But you could just look for the non-fractions without using conditional formatting.
I tend to have many rows, each with a simple process. It makes things easier to follow. But this does mean that often the end result is no longer in view when I'm looking at the start of the row. I get around this by making the first column just a repeat of the end result. I can then see solutions and start values side by side.