Vessels received by the brother monarch > An eastern monarch sends 10.000 golden vessels to a brother monarch, whose kingdom is many days march distant. The gift is carried on camels. Each merchant who supplies camels for some part of the journey, demands as commissions 10% of what passes through his hands. Thus the first merchant hands over to the second 9.000 golden vessels. Altogether the vessels pass through 20 merchants. How many vessels does the brother monarch receive at the end? -- W.W Sawyer "Mathematician's Delight" The time consuming solution is to manually calculate all the values, but there must be a logarithmic rule/formula that can used to find the result quickly for any number of merchants (without writing a computer program).

Each time the vessels pass through a merchant, their number is multiplied by $.9$. Thus after $20$ merchants, the number of vessels is multiplied by $.9^{20} \approx 0.12158$. So in the end you have $10000(0.12157665459) \approx 1215.8$ vessels.