Question 3.1.4

This problem is from Fibonnaci’s Liber Abaci, written in the year $1202$. Imagine you have a pair of young rabbits (a male and a female) and after a month they mature into adult rabbits. Every month after that they breed and produce another young pair of rabbits. The young rabbit pairs similarly take a month to mature, then start producing another pair of young rabbits every month. So in the first month we have $1$ pair, in the second month still only $1$ pair (now adults), in the third month $2$ pairs ($1$ adult, $1$ young), in the fourth month $3$ pairs ($2$ adult, $1$ young), in the fifth month $5$ pairs ($3$ adult, $2$ young), and so on. Find the number of pairs of rabbits in the twelfth month. Show answer