Female rabbits are either juvenile or adult. Each month, each juvenile grows to adulthood and each adult female gives birth (on average) to one juvenile female. Starting with one juvenile female rabbit, how many female rabbits will there be after 10 months ?
Female rabbits are either juvenile or adult. Each month, each juvenile grows to adulthood and each adult female gives birth (on average) to one juvenile female. Starting with one juvenile female rabbit, how many female rabbits will there be after 10 months ? Correct Answer 89
Concept of Fibonacci series is used:
The Fibonacci sequence is a set of numbers that starts with a one or a zero, followed by a one, and proceeds based on the rule that each number (called a Fibonacci number) is equal to the sum of the preceding two numbers. i.e. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on
Let us assume there is one female juvenile rabbit, initially.
When the rabbit is one month old, it matures to become an adult female rabbit and gives birth to another female rabbit.
Number of female rabbits in nth month is equal to the sum of female rabbits in (n – 1)th month and (n – 2)th month.
When this process continues till 10 months, below are details of number of rabbits at the end of each month.
At the start 1 juvenile
1st month - 1
2nd month - 2
3rd month - 3
4th month - 5
5th month - 8
6th month - 13
7th month - 21
8th month - 34
9th month - 55
10th month - 89
∴ 89 female rabbit were there after 10th month