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**tt****Member**- Registered: 2005-07-03
- Posts: 32

I found this puzzle on web, no solutions :

Supposed that every 2 mature rabbits reproduce 2 baby rabbits each month and baby rabbits will be mature and reproduce after 2 months.

How many rabbits will you have after 10 months if you start with 2 mature rabbits ?

*Last edited by tt (2005-07-14 17:44:51)*

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,409

This is much more complicated than what I thought!

*Last edited by ganesh (2005-07-14 18:54:00)*

Character is who you are when no one is looking.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Work out how many rabbits you get over the first few months. Notice any patterns?

*Works out answer* Oh, that's gross!

Why did the vector cross the road?

It wanted to be normal.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,409

You mean 144? My friend says it is ___!

*Last edited by ganesh (2005-07-14 19:42:20)*

Character is who you are when no one is looking.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Yes, but it was meant to be a subtle hint.

And I've just realised I'm wrong, anyway.

To MathsIsFun, the mature rabbits breed every month, not every two.

Why did the vector cross the road?

It wanted to be normal.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

0 months: 2 Adults, 2 Babies

2 months: 4 Adults, 4 Babies

4 months: 8 Adults, 8 Babies

...

Huh? Is it that simple ... I must have made a mistake.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

120 rabbits?

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**justlookingforthemoment****Moderator**- Registered: 2005-05-26
- Posts: 2,161

172 rabbits?

mathsyperson wrote:

Notice any patterns?

Fibonacci!

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

This is becoming very interesting. I get 178.

Why did the vector cross the road?

It wanted to be normal.

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

Okay, assume we start with a malefemale pair and all babies are born as male-female pairs.

AA = Adult (mature) pair, JJ = Juvenile (one-month old) pair, BB = Baby (newborn) pair

Starting with AA:

Total rabbits at end of 10 months = 2×(28 + 13 + 19) = 120.

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

All right, I see something there. I have assumed that the rabbits become mature at the end of two months, but dont start reproducing at two months yet i.e. they start reproducing only in their third month. (I mean, Ive assumed that the rabbits are born at the end of each month and reach maturity *at the end of* two months so they wouldnt have time yet to reproduce.)

EDIT: Anyway, Ive just made a re-calculation on the revised assumption that the juveniles can reproduce as soon as they reach maturity (just add a blue arrow from each JJ to the BB below it in my diagram above). Guess what answer I got.

288.

*Last edited by JaneFairfax (2007-03-17 12:28:12)*

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**justlookingforthemoment****Moderator**- Registered: 2005-05-26
- Posts: 2,161

Haha, I can't add properly! I actually got 178 too.

Oops, my bad!

What I think:

```
month a j b t
1) 1 1
2) 1 1 2
3) 1 1 1 3
4) 2 1 2 5
5) 3 2 3 8
6) 5 3 5 13
7) 8 5 8 21
8) 13 8 13 34
9) 21 13 21 55
10) 34 21 34 89
```

With the letters representing the same things as Jane's, in pairs. And 't' being the total number of pairs.

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

The month numbers you have there are for the *beginning* of the month. Thus your month 10 would mean beginning of that month, meaning only 9 full months have passed. Since the question wants 10 months, I think you should add another months calculation
which should bring the total number of rabbits to 288.

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**justlookingforthemoment****Moderator**- Registered: 2005-05-26
- Posts: 2,161

Yes, I see. If the month numbers there are for the end of the month, I have assumed that the rabbits don't reproduce in the first month. So, do the rabbits reproduce in the first month?

EDIT: Actually, I suppose they would. I think you're right. Ganesh even said the number of pairs at the start, didn't he?

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