100-days-of-rust/Week-09/Day-63_The-Rabbit-Problem/README.md

# The rabbit problem

Rabbits are known for their fast breeding, but how soon will they dominate the earth?

Starting with a small population of male and female rabbits we have to figure out how long it will take for them to outnumber humans 2:1.

Every month a fertile female will have 14 offspring (5 males and 9 females).

A female rabbit is fertile when it has reached the age of 4 months, they never stop being fertile.

Rabbits die at the age of 8 years (96 months).

## Input Description

You will be given a list of numbers as following:

```text
Male_rabbits Female_rabbits Rabbits_needed_alive
```

The initial rabbits will always be 2 months old and fertile females will always produce 14 offspring (5 male, 9 female)

Every month that passes things should be done in this order:

    Fertile female reproduce (so 7 year & 11 months old will reproduce)

    rabbits age (except newborn) (and rabbits reaching 8 years will die, the 7 year & 11 months old will die)

fx:
```text
2 4 1000000000
```

## Output Description

You output how many months it took for world domination.

## Example

Looking just at the female population:

```text
we start with 1 female with the given starting age of 2 months

the index is their age (0-index is 0 months old)
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0] Month 0
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0] Month 1
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0] Month 2
[ 9, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0] Month 3
[ 9, 9, 0, 0, 0, 0, 1, 0, 0, 0, 0] Month 4
[ 9, 9, 9, 0, 0, 0, 0, 1, 0, 0, 0] Month 5
[ 9, 9, 9, 9, 0, 0, 0, 0, 1, 0, 0] Month 6
[ 9, 9, 9, 9, 9, 0, 0, 0, 0, 1, 0] Month 7
[90, 9, 9, 9, 9, 9, 0, 0, 0, 0, 1] Month 8

```

## For inspiration 

[The rabbit problem](http://go-here.nl/the-rabbit-problem.html)

**Challenge input(s)**
```text
2 4 1000000000
```
```text
2 4 15000000000
```


**Challenge output(s)**
```text
32
```
```text
36
```

**Bonus**

Tell how many dead rabbits there are when they dominate earth.