Please turn on javascript in your browser to play chess.
Posers and Puzzles

Posers and Puzzles

  1. 01 Jun '05 21:04 / 1 edit
    Husband and Wife A and B have three daughters C D and E

    C D and E marry, and have 6 children between them

    A and B say "3 children and 6 grandchildren have descended from us, we have increased the world population"

    Are they correct?
  2. 02 Jun '05 00:14
    Originally posted by iamatiger
    Husband and Wife A and B have three daughters C D and E

    C D and E marry, and have 6 children between them

    A and B say "3 children and 6 grandchildren have descended from us, we have increased the world population"

    Are they correct?
    There would need to be 8 grandchildren for them to be certain that the lineage has been replaced.
  3. Standard member PBE6
    Bananarama
    02 Jun '05 01:15 / 1 edit
    Originally posted by iamatiger
    Husband and Wife A and B have three daughters C D and E

    C D and E marry, and have 6 children between them

    A and B say "3 children and 6 grandchildren have descended from us, we have increased the world population"

    Are they correct?
    As far as I know, the long-term birth rate needed to keep the population steady is slightly over 2 children per couple (somewhere around 2.3?). If every couple had 2 kids that lived, it would be perfect. However, we need the extra little bit to make up for accidental deaths, disease, etc...

    So over the first generation, parents A and B have slightly over-contributed to the population. Over the second generation, kids C, D and E (really couples C, D and E) have slightly under-contributed to the population. In a perfect world, A and B would give birth to C and D, who would later marry C2 and D2 and give birth to E, F, G and H (2 kids per couple, total of 6 "offspring" of A and B and 2 spouses, 10 people total). In a slightly more realistic world, A and B would give birth to 2.3 kids, who in turn would marry 2.3 spouses and give birth to 2.3 kids each, for a total of 11.5 people.

    In this example, the total number of people is 14 (A, B, C, C2, D, D2, E, E2, F, G, H, I, J and K), so they have slightly increased the world's population (if everyone else had 2 kids per couple).

    Assuming no one died, then there would be a net increase. However, if you take the qestion to mean "what if everyone carried on the way this family did" then it depends on the death rate and the sampling/averaging rate. For example, if there were a nuclear holocaust and everyone died except for this family, then the family could theorectically (a) increase the population (addition of C, D and E counting before the deaths); (b) decrease the population (everyone else dies, add 14 people to the mix, net decrease in population); or (c) keep it the same (sample taken after 14 people died, net equilibrium in population).

    Pedantic, I know, but still important if you were ever to carry out a pratical census, ain't it?!? Practical being taking a census in the middle of a nuclear holocaust.

    ...

    Whatever!!! It's still up in the air.
  4. Standard member The Plumber
    Leak-Proof
    02 Jun '05 12:37
    Originally posted by iamatiger
    Husband and Wife A and B have three daughters C D and E

    C D and E marry, and have 6 children between them

    A and B say "3 children and 6 grandchildren have descended from us, we have increased the world population"

    Are they correct?
    Depends on one's assumptions....

    For example, let's make these four assumptions:

    1 - on average, the birth rate of men and women is essentially equal
    2 - on average, people live to be old enough to reproduce (i.e., A&B live in a society with modern medical care, and can be fairly certain their offspring will survive long enough to produce offspring - which, in fact, has occurred).
    3 - the marriage (or at least coupling/offspring production) rate is 100%
    4 - the fertility rate is 100%

    If the world population were 100 people (50 couples), and everyone acted the same as A&B (having 3 children, not necessarily 3 daughters), then generation 2 would have 150 people, and if generation 2 acted the same as C, D, & E, then generation 3 would have 150 people.

    As PBE6 has pointed out, there is good reason to doubt some of these assumptions. However, if his assumption is correct that fertile couples need to average 2.3 kids to make up for un-reproductive people (infertility, single, kids who don't make it to adulthood, etc.), then A&B should have 5.29 grandchildren (2.3 x 2.3). The required replacement rate would have to exceed SQRT(6) (or 2.45) for A&B to not have produced enough offspring to maintain the replacement rate at the grandchild generation. (at least, I think that's the case)

    By the way, if A&B are questionable, what about my wife's parents? They have 9 kids and 28 grandkids (4 of whom are adopted, so biologically 24 grandkids). Is that sufficient for them to say they have increase the world population?
  5. 02 Jun '05 15:16
    Of course.

    Say the worlds population is 6 billion including A and B, after the kids there are 6 billion and 9.

    Depends how you define population I guess.
  6. Standard member The Plumber
    Leak-Proof
    03 Jun '05 02:00
    Originally posted by tommyg007
    Of course.

    Say the worlds population is 6 billion including A and B, after the kids there are 6 billion and 9.

    Depends how you define population I guess.
    Of course if A&B (and kids) are the only ones generating offspring, in the time it takest to get the 6 grandkids, we've probably lost about 2 billion or so of the 6 billion, so we're left with 4 billion and 9 - A&B better take some serious fertility drugs....