Puzzler #5

[ccb_v2 0]

A pair (male and female) of rabbits were born on June 1, 1995 and placed in a walled enclosure to breed. If a pair of rabbits produces another pair of rabbits at the end of their first two months and after that produces another pair of rabbits every month, and if each pair of rabbits produced follows this same pattern, then how many pairs of rabbits will there be in the walled enclosure June 1, 1996? Assume that no rabbits in this enclosure die during the year.

[Killer008r 0]

I know the answer should i post it here or pm you?

[Houdini 0]

82 if at least one female was born the first month.24 22 20 18 16 14 12 10 8 6 4 2 (one set breeders)14 12 10 8 6 4 212 10 8 6 4 210 8 6 4 28 6 4 2 6 4 24 22 (seven sets breeders)---82The female matures and is ready for breeding at 5 months with a gestation period of 31 days. If both the first kits born were male then it would only be 80, male kits are mature bor breeding at 6 months.

[sagech 0]

hmm... This resembles Fibonacci numbers perfectly. The first 12 Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89. So the number of baby rabbits produced is 232. Adding this to the original parents, the answer is 234. Is that correct?

[Houdini 0]

Look closely at the above answer, which is 82 rabbits unless the first pair born in the firs month are both male then there would be 80. until month 6 there can be new kits born only to the origional pair (which will produce 24 rabbit kits over a 12 month period, add to that the total of the breaders that if born the first month take a total of 5 months to be ready to breed then another month before the kits are born to add two more to the 12 which is 14 but ony starting in month 6 the totals on the left are to be added in the left most column from top to bottom, at the end of 12 months there will at most be seven sets of breeding rabbits. If you look at the table closely you should see the correlation, it is hard to make a table properly without using the <table><tr><td> tags other wise I would have shown month by month how the total was arrived at and how many were actually breeing to add to the population.

[sagech 0]

This link might clear up the problem: http://www2.surrey.ac.uk/feps/departments/

[sagech 0]

Sorry for double posting.

 

hmm... This resembles Fibonacci numbers perfectly. The first 12 Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89. So the number of baby rabbits produced is 232. Adding this to the original parents, the answer is 234. Is that correct?

1064337807[/snapback]

I think I made mistake here. Since the first pair of kits are produced at the end of the 2nd month, the series should be 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233. So, at the end of the 12 month period, there will be 233 pairs of rabbits.

[Jeigh1405241495 0]

Gotta lov the Fib's We did this problem in my combinatorial theory class this year (just in some more detail). Those FIb numbers show up in alot of places you wouldn't expect them to :|

[Houdini 0]

The only real problem with the question or puzzle is that with the smaller breeds of rabbits a doe can not breed till she is 5 months old and the buck is not ready to breed til he is 6 months old, in the link above it stated that there would be a male and female pair borm the first month and that that pair would breed the second month and produce an additional pair of kits. The larger breeds take 6 months to mature for breeding, so my answer was based on that reality, and to learn more about gestation and maturation of rabbits try this link. Breeding Rabbits I believe the way the question was worded left it to my interpretation of how rabbits actually breed and the maturaional realities involved.