You start with one pair of brand new baby rabbits, a boy and a girl. Rabbits are old enough to have babies of their own when they are one month old. So, a female rabbit can give birth to a new pair at the end of her second month.
If rabbits never die and each female has one new pair (one male, one female) every month from her second month on, how many pairs of rabbits will you have after one full year?
Check if you were right - full answer with solution below.
Solution :
At the start (Month 0): You have 1 pair. They are babies.
End of Month 1: They are now one month old and can mate. You still have only 1 pair.
End of Month 2: The original female gives birth. You now have the original pair + 1 new pair = 2 pairs.
End of Month 3: The original female gives birth again. The other pair is still too young. You have 2 pairs + 1 new pair = 3 pairs.
End of Month 4: The original female gives birth again. The pair born in Month 2 is now old enough to have its first baby. You have 3 pairs + 2 new pairs = 5 pairs.
If we write down the number of pairs at the end of each month, we get a famous pattern: 1, 1, 2, 3, 5, ...
This is the Fibonacci Sequence, where you get the next number by adding the last two numbers together (for example, 2 + 3 = 5).
Let's continue this for all 12 months:
- Month 1: 1 pair
- Month 2: 1 pair
- Month 3: 2 pairs
- Month 4: 3 pairs
- Month 5: 5 pairs
- Month 6: 8 pairs
- Month 7: 13 pairs
- Month 8: 21 pairs
- Month 9: 34 pairs
- Month 10: 55 pairs
- Month 11: 89 pairs
- Month 12: 144 pairs (Because 55 + 89 = 144)
Final Answer
At the end of one year, you will have 144 pairs of rabbits.
(That's a total of 144 x 2 = 288 rabbits!)