MathDB

In a Greek village of

100

inhabitants in the beginning there lived

12

Olympians and

88

humans, they were the first generation. The Olympians are

100\%

gods while humans are

0\%

gods. In each generation they formed

50

couples and each couple had

2

children, who form the next generation (also consisting of

100

members). From the second generation onwards, every person’s percentage of godness is the average of the percentages of his/her parents’ percentages. (For example the children of

25\%

and

12.5\%

gods are

18.75\%

gods.) a) Which is the earliest generation in which it is possible that there are equally many

100\%

gods as

0\%

gods? b) At most how many members of the fifth generation are at least 25% gods?

Problem Statement