Let's consider the connexion between two persons from the mothers' side and count the possibilities to express it. E.g., if the connexion is only 1 generation, then there is only 1 possibility to express it:
- the mother.
If the connexion is 2 generations, then there are 2 possibilities to express it:
- the mother of the mother
- the grandmother.
If the connexion is 3 generations, then there are 4 possibilities to express it:
- the mother of the mother of the mother
- the grandmother of the mother
- the mother of the grandmother
- the great-grandmother.
If the connexion is 4 generations, then there are 7 possibilities to express it:
- the mother of the mother of the mother of the mother
- the mother of the mother of the grandmother
- the mother of the grandmother of the mother
- the grandmother of the mother of the mother
- the grandmother of the grandmother
- the mother of the great-grandmother
- the great-grandmother of the mother.
Now, if the connexion is 100 generations, how many possibilities are there to express it by using only the words "mother", "grandmother", "great-grandmother", "the" and "of"?
Calculate the same for 1000 generations. Can you have the answer in less than 10 seconds? (10'' of computer calculations)
Here is my answer.
Update:
Damn it! I have just guessed an algorithm, that can calculate this in linear time and in less that 1 sec! Can you guess it too? ;o)
Here is my second answer.