I came up with an awesome math/logic problem stoned.

I came up with an amazing and really interesting (in my opinion) math/logic problem tonight while smoking a bowl and buzzing on a 30mg extended release adderall. Here it is, try and figure it out and if no one can after awhile I'll post the solution.

Suppose for some reason that the entire population of humans is nearing extinction. There are 4 humans left alive, all unrelated to each other. 2 males, and 2 females, all 18 years old. They are told to repopulate the planet without any inbreeding. For the sake of morality, step family (step siblings, parents, grandparents, great grandparents, children, grandchildren, great grandchildren, cousins, nephews, nieces, etc.) cannot breed together.

-Each male and female will be fertile until they are 37.
-A man can only have children with each woman two seperate times (So, a man and a woman will have a maximum of 4 children with each other).
-Whenever a woman gets pregnant and has children, it will always be twins and they will be a boy and a girl.
-When a child reaches 18 years of age, they will have their first children. They will have their second children when they reach 36 years of age.
-People die at the age of 73.

Using this information, answer the following:

[1] How many generations can these 2 families live for until there are no more possible unrelated combinations of males and females able to produce?

[2] How many people will have been alive after everyone dies out?

[3] What will have been the most people alive at one time?

[4] How many years will these people survive for?

It really isn't that easy, I was so focused on figuring this out though because of this Adderall that I sat down for at least an hour or more and wrote and drew out 2 family trees. I'll explain later how I came up with this problem. Bonus points if you can come up with hypothetical family trees. I'll translate mine to the computer and post it later.

whoa man thats crazy, i probably could figure it out but i am way too lazy :D and i cbf but meh, its still cool :)

alright i tryed to figure it out lol it gave me a head ache....i give up :( stupid maths

man what the fuck kind of weed were you smokin when you came up with that ?

Holy shit.

....Somebody is probably figuring it out as we speak.

That's some college grade shit right thurr!

i dont know if ive done it right but
1) can the grandchildren (2nd generation of children) have children with the original parents?

2)I dont think they would die out....because they would be creating new families....or somthing?? lol

3)36

4)72

5) i suck at math....but thanks for getting my brain a little active :)

Haha, ok. There is a numerical answer for every question. They will not continue to produce forever, eventually there will be a point where there are no more possible male/female combinations unless they breed with a relative. And the 3rd generation (first generation of grandchildren) cannot breed with the other family's original female (the one that would be the equivalent of their grandmother except in the other family) because the female would be 54 years old and infertile by the time the grandchildren reach 18, the age of maturity.

Hint: The fact that females can only have 4 children per male has a lot to do with it.

Oh and both your answers are wrong Az, but good try. ;)

Thanks LittLeWinG, and it's not too hard, just takes some time.

highjinx, I like to call it philosophical weed, or the thinking man's herb. :D

STDz, I'm a second year college student so that might explain why. :P

If a few more people respond and can't figure it out I'll post the solution. To be completely honest I'm insanely proud of coming up with this. I also came up with an experiment I'm going to write up (that's where this problem came from) and if I could ever get enough research grants and a few willing volunteers I would love to try it and write a book on it. This problem is fucking proof why pot should be legalized. I would've never thought of something this complex and thought out if I did not smoke.

cool i want to hear what your experiment is.....i love experiments....LOL>....

Here's a mind tickler-

1st-purchase large feather
2nd-insert into ear
3rd-poop

Sleep is for the weak.

How can it be that they can only have kids at ages 18-37?
That means they can only have kids twice in their lives...
By your own rules every COUPLE is sposed to have kids TOGETHER twice in their life...
Does that mean that every individual can have kids only with 2 others?

I may have confused myself there...all the above disregarding the rule of no interbreeding...We're taking that for granted...I'd really like to try and figure this out if you could gimme some info!!! :)

Dun take me wrong...all the above is subject to mistake...I'm no mathematician..

Excuse me...by my calculations...every individual can have kids only with one other individual during their lives not 2 as I said above

oh my head hurts :(

And well I'm really ashamed but if I'm making a mistake here could you gimme the slightest of hints about what it may be?

Pwease

dude you left your weed in the math department didnt you. thats why you have these trippy problems

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Originally Posted by Caruso329

They are told to repopulate the planet without any inbreeding. For the sake of morality, step family (step siblings, parents, grandparents, great grandparents, children, grandchildren, great grandchildren, cousins, nephews, nieces, etc.) cannot breed together.

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Why did they have to be told? Told by whom, Readers Digest?

Haha okay guys, stop trying to read so deep into this. This is just a fucking HYPOTHETICAL situation. I just came up with those rules (18 and 36 breeding for example) to add some structure to the problem and to make it more difficult.

And every male can (and should, if you want to figure out the answer) have sex with every female in the other family that he isn't related to in some way. If they share the same aunt or are cousins for example, they cannot breed. Same goes for step-relations.

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Originally Posted by OlympianBud

How can it be that they can only have kids at ages 18-37?
That means they can only have kids twice in their lives...
By your own rules every COUPLE is sposed to have kids TOGETHER twice in their life...
Does that mean that every individual can have kids only with 2 others?

I may have confused myself there...all the above disregarding the rule of no interbreeding...We're taking that for granted...I'd really like to try and figure this out if you could gimme some info!!! :)

Dun take me wrong...all the above is subject to mistake...I'm no mathematician..

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In order:
-Because I said they could! ;) If you really want a reason, then they're too busy raising the children they have now to have any more until their current ones have matured.

-You're on to something there Olympian, I can't really answer this without giving it away.

Good luck, and I'll probably post the solution later tonight or tomorrow.

[1] How many generations can these 2 families live for until there are no more possible unrelated combinations of males and females able to produce?
Three generations: The original four, their kids, and grandkids.

[2] How many people will have been alive after everyone dies out?
The four originals, their 16 children, and the 128 grandkids. Total - 148.

[3] What will have been the most people alive at one time?
148 - the originals being 72, their first children being 54, their second children being 36. The first set of grandkids being 18, and the second set having just been born.

[4] How many years will these people survive for?
In total, from the origainl four at 18, to the grandkids deaths; 127 years.

[EDIT] Not sure about the answers to three and four now.

[EDIT] Update to last post.

[3] 4 originals, 16 kids, 64 grandkids.

[4] 84 people alive.

My brain aches, please tell me I got it right?!

ohh psychopixi you are soooo close. Solution to come after I'm done with my classes today.. so in maybe 7-8 hours? Haha, soo close psychopixi. You're definitely on the right track, but the 16 (2nd generation) will not produce 64 children. I think you're just trying to turn it into a simple equation, which it's not that simple. Go back and check some of your pairings with the 2nd generation. Remember, if Jack mates with Jill, then you have to make sure Jill's dad, mom, aunts, uncles, grandparents, great grandparents, great great etc. are not tied to Jack's side of the family at all.

Okay... so I have 7 or so hours to crack this. *determined* how about this...

How about the children of the original four mate with each other - to give 64, and with the one of the original four who is of the opposie sex and not a parent, giving an extra 64.

Say the original four are Ma, Fa, Mb and Fb.

Ma and Fa have M1, M2, F1, and F2.
Ma and Fb have M3, M4, F3 and F4.
Mb and Fa have M5, M6, F5 and F6.
Mb and Fb have M7, M8, F7 and F8.

That's 16 kids.

Ma and Fa's kids have to mate with Mb and Fb's kids to ensure no incest occurs.
Mb and Fa's kids have to mate with Ma and Fb's, for the same reason.

M1 mates with F7 and F8, four kids with each gives eight kids.
M2 mates with F7 and F8, four kids with each gives eight kids.
Total 16, so far.

F1 and F2 mate each mate with M7 and M8.
16 kids from those unions giving us 32 grandkids now.

M3 and M4 each mate with F5 and F6, giving us 16 more kids, and a running total of 48 grandchildren.

F3 and F4 each mate with M5 and M6, giving us yet another batch of 16 grandkids, and a running total of 64.

How'm I doing so far?

THEN; M1 and M2 mate with Fb (Fa was their mother). This gives us eight more kids.
F1 and F2 mate with Mb (Ma was their father). Eight more.
Running total is now at 64 plus 16, is 80.

M3 and M4 mate with Fa, and F3 and F4 mate with Mb.
Running total is 80 plus 16, is 96.

M5 and M6 mate with Fb, and F5 and F6 mate with Ma.
M7 and M8 mate with Fa, and F7 and F8 mate with Ma.

Running total is now 96 plus 32, is 128.

That's 128 grandchildren, 16 children and the 4 originals. 148 people.

I love Math so much to the point that I don't need your stupid math problem.

I'm only kidding, I'm just pointing out that I'm lazy and would rather play PS2.

My answer to your problem is, 72, 562, 12 1/2, 352. My question is: How many times can you take 1 nanogram off of a bowl of Marijuana and still wind up with less than a half an ounce?

Quote:

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Originally Posted by psychopixi

Okay... so I have 7 or so hours to crack this. *determined* how about this...

How about the children of the original four mate with each other - to give 64, and with the one of the original four who is of the opposie sex and not a parent, giving an extra 64.

Say the original four are Ma, Fa, Mb and Fb.

Ma and Fa have M1, M2, F1, and F2.
Ma and Fb have M3, M4, F3 and F4.
Mb and Fa have M5, M6, F5 and F6.
Mb and Fb have M7, M8, F7 and F8.

That's 16 kids.

Ma and Fa's kids have to mate with Mb and Fb's kids to ensure no incest occurs.
Mb and Fa's kids have to mate with Ma and Fb's, for the same reason.

M1 mates with F7 and F8, four kids with each gives eight kids.
M2 mates with F7 and F8, four kids with each gives eight kids.
Total 16, so far.

F1 and F2 mate each mate with M7 and M8.
16 kids from those unions giving us 32 grandkids now.

M3 and M4 each mate with F5 and F6, giving us 16 more kids, and a running total of 48 grandchildren.

F3 and F4 each mate with M5 and M6, giving us yet another batch of 16 grandkids, and a running total of 64.

How'm I doing so far?

THEN; M1 and M2 mate with Fb (Fa was their mother). This gives us eight more kids.
F1 and F2 mate with Mb (Ma was their father). Eight more.
Running total is now at 64 plus 16, is 80.

M3 and M4 mate with Fa, and F3 and F4 mate with Mb.
Running total is 80 plus 16, is 96.

M5 and M6 mate with Fb, and F5 and F6 mate with Ma.
M7 and M8 mate with Fa, and F7 and F8 mate with Ma.

Running total is now 96 plus 32, is 128.

That's 128 grandchildren, 16 children and the 4 originals. 148 people.

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I tried doing it exactly the same way and it started working out so I guessed that'd have to be it and never calculated to get the final numbers...

But since you bothered it'll have to be this

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Originally Posted by beachguy in thongs

I love Math so much to the point that I don't need your stupid math problem.

I'm only kidding, I'm just pointing out that I'm lazy and would rather play PS2.

My answer to your problem is, 72, 562, 12 1/2, 352. My question is: How many times can you take 1 nanogram off of a bowl of Marijuana and still wind up with less than a half an ounce?

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Many