Investigation techniques

It often helps to examine a much simpler version of the same basic problem, and then take the smallest possible development steps towards the problem you really need to answer.

The simplest version of More Beads might be to have just two people and no commission for the bead sharer.

You could then develop by adding commission of 1, 2, 3 etc.

Or instead develop by going to three people and still no commission. Then four people, and so on.

Another useful technique is reversal (working backwards)

Start with the number in the final share and work the calculations in reverse (using the spreadsheet to do the calculations of course!)

If you have found out all about this arrangement, how about investigating other systems for sharing?