The Rabbit Problem

In the year 1202, Fibonacci became interested in the reproduction of rabbits. He created an imaginary set of ideal conditions under which rabbits could breed, and posed the question, "How many pairs of rabbits will there be a year from now?" The ideal set of conditions was a follows:

1. You begin with one male rabbit and one female rabbit. These rabbits have just been born.
2. A rabbit will reach sexual maturity after one month.
3. The gestation period of a rabbit is one month.
4. Once it has reached sexual maturity, a female rabbit will give birth every month.
5. A female rabbit will always give birth to one male rabbit and one female rabbit.
6. Rabbits never die.

So how many male/female rabbit pairs are there after one year (12 months)?

A Rabbit

Month #0 - At the beginning of the experiment, there is one pair of rabbits (condition #1).

Month #1 - After one month, the two rabbits have mated but have not given birth. Therefore, there is still only one pair of rabbits.

Month #2 - After two months, the first pair of rabbits gives birth to another pair, making two pair in all.

Month #3 - After three months, the original pair gives birth again, and the second pair mate, but do not give birth. This makes three pair.

Month #4 - After four months, the original pair give birth, and the pair born in month #2 give birth. The pair born in month #3 mate, but do not give birth. This makes two new pair, for a total of five pair.

Month #5 - After five months, every pair that was alive two months ago gives birth. This makes three new pair, for a total of eight.

How do we solve this problem to forecast the number of pairs of rabbits many months from now? See the Proof page to learn how.