Housecat Reproduction

[Hornbein]

Start with one hundred housecats. Given unlimited resources, in seven years you will have a billion housecats.

 

[pinball1970]

Start with one hundred housecats. Given unlimited resources, in seven years you will have a billion housecats.

Are they all female?

 

[pinball1970]

Start Jan 1st. For one female cat they can have 20 kittens in a year, average 4 litters and 5 kittens per litter.
Kitten can reach puberty at 4 months so they start contributing by August, 25 kittens between them.
There must be a geometric series that can do this easier than brute forcing it.

 

[Hornbein]

Are they all female?

If they were then after seven years you would have at most 100 housecats.

 

[pinball1970]

If they were then after seven years you would have at most 100 housecats.

"given unlimited resources" I took to mean access to males as well as Whiskers.

 

[pinball1970]

If they were then after seven years you would have at most 100 housecats.

So its a 50/50 split? 80/20? 95/5? It makes a difference.

 

[DaveC426913]

By the time there is 0.001% of that number, they won't be housecats any longer. They'll be yardcats and streetcats.

 

[256bits]

2 ³⁰ = 1,073,741,824

Each litter of 4 kittens in average 2 of each sex.
Only the female can reproduce, on average again every 4 months.

I would guessimate that starting with 100 cats, approx 2 ⁸ = 128
then we have 9 years of cat production
( 2 years initial for the 100 cats + 7 more years

2 to the 8 for the 100 cats + 2 to the 28 for 7 years
2³⁶ = 68,719,476,736 female cats + kittens
plus the same amount of male cats + kittems

Total == 137,438,953,472 domestic felines

Number of litter boxes unknown

 

[DaveC426913]

At an average of 18" in length (not including tail) and 4" width, that's exactly 2 cats per square foot, assuming a face-centred cube packing lattice.
137,438,953,472 cats would entirely fill a square 50 miles on a side.