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The investigation offered this month is called More Beads, and follows on from Beads. Ituses Excel to run off the calculated values leaving your mind free to observe and account for the patterns produced by that process.

A heap of beads was shared out between three people by a professional bead sharer. The first person got one third, but not before the bead sharer had taken one bead as commission. The second person had one third of what remained, but again, after commission of one bead had been taken by the bead sharer. The third person also received a one third portion of what remains but, as before, after commission. Once all three people had received beads the bead sharer took a final commission of one bead and shared the remaining beads equally between the three people. There were no beads left over and no beads were split into fractions. How many beads could there have been at the start?

For example there could have been 3562 beads. Try it.
You should see 3562 becoming 2374, then 1582, then 1054, and finally three equal shares of 351.

Mathematical modelling. Probability distributions, expectation and variance. Random variables. Conditional probability. Spreadsheets. Approximate solution by numerical methods.. Summation of series. Tree diagrams. Theoretical probability. Experimental probability.