A Problem of Population

            If human beings did not die the earth would sooner or later be overcrowded with the progeny of human life, within a score of years or so our continents would be teaming with millions of people fighting each other for living space.

              Let us take for instance the case of two cases of couples today. supposing each of these couple give birth to 4 children and the eight children in turn form 4 couples and each couple in turn give birth to 4 children, and those 16 children again form eight couples and give birth to 4 children each and so on, can you tell exactly the number of progeny the two initial couples would have after 10 generations?

Answer:   8184 – We start out with 2 couples, four people or 2² people who increase their progeny as follows:

2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷ + 2⁸ + 2⁹+ 2¹⁰ + 2¹¹ + 2¹² = 8184