Counting the ancestors of honeybees4
Honeybees (henceforth referred to as bees) have a very peculiar characteristic: a male bee has just one parent. This has a very interesting consequence as we are about to see. A male bee has only one parent: a female bee. A female bee has two parents: a male bee and a female bee. To count the number of ancestors of a male bee, observe that:
- It will have 1 parent bee which will be a female
- Considering that there is 1 female parent bee, there’ll be 1 male bee and 1 bee female because of female child: there will be 2 grandparents
- There will be 1 female parent because of 1 male bee and 1 male parent and 1 female parent because of 1 female child: there will be 3 great-grandparents
- There will be 2 pairs of male and female bees because of 2 children female bees + 1 female bee because of 1 male child: there will be 5 great-great-grandparents There will be 3 pairs of male and female bees because of 3 female children + 2 female bees because of 2 male children: there will be 8 great-great-great-grandparents
Similarly, counting the number of ancestors of a female bee and tabulating the results below we see an interesting phenomenon:
| Gender | # parents | # grandparents | # great-granparents | # great-great-granparents | # great-great-great-granparents |
|---|---|---|---|---|---|
| Male | 1 | 2 | 3 | 5 | 8 |
| Female | 2 | 3 | 5 | 8 | 13 |
