Edward Lai Harner, Edward Harner
Andrea Harner
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January 21, 2005

Mensa Me Crazy

Fellow Mensans,

There's one question that is stumping me!!

In the early 18th century Mrs. Abigail Eischrank of Cambridge, MA, gave birth to thirteen children. Exactly half of them were girls. Explain.

Please don't say, "one was a hemaphrodite!" or "one was still born." I just don't think that's it. Only non-retarded answers will be included in the brilliant thread of possible answers.

These cards were a great gift to Jonah by Chelsea and they do not contain answers therefore I'm asking you.



Could it be that they were all girls? Or more than 7 of them were girls? Under both of these conditions "exactly half of them" would still be girls. The sentence doesn't exclude this possibility... does it?

Posted by: C.K. Sample, III at January 21, 2005 12:42 AM

Hi there. Was checking out pictures of Howard Dean on images.google.com and yours was on one of the first two or three pages.

You are soooo cute. I was heartbroken when I read elsewhere on your blog that you're married. Oh well, lucky guy that man!

Have you written any books?
Just curious.
I'm thinking of writing a book this year.

Anyway, nice blog and stay warm -- I heard there is a winter storm coming!

(Did you watch the inauguration?)


Posted by: Jerome Wiley Segovia at January 21, 2005 1:32 AM

Sorry, forgot to add my guess for the riddle.

I don't think that "all of them were girls so the statement is still true" is right. Because it says "exactly", so "more than half" is not exactly.

It might have something to do with identical twins somehow, or maybe the uncertainty principle?


Posted by: Jerome Wiley Segovia at January 21, 2005 1:43 AM

7 were girls -- "them" refers to the entire group, including Abby.

Posted by: Della at January 21, 2005 2:41 AM

della is right

Posted by: bal at January 21, 2005 3:35 AM

Yes. Della is right. I'm an idiot...

Posted by: C.K. Sample, III at January 21, 2005 10:45 AM

The answer may be what the author intended but it is hardly correct. Here's why. If the word "them" relates the mother and, thus, the household, it must include the father as well Note the mother's name, "Mrs. Abigail Eischrank." Abigail is married and the household or family unit would include a father, especially in the early 18th century.

Now, you respond, she's a widow. But the proper way to address a Widow is either:

Ms. Abigail Eischrank or
Mrs. [Husband's first name] Eischrank

In fact, a women should never be addressed as Mrs. Abigail Eischrank.

So, the correct answer is the question is flawed and move on.

Posted by: Bob at January 21, 2005 11:47 AM

it still doesn't make any since...speaking of MA, did you guys see who didn't vote for condi :o)

Posted by: mike d at January 21, 2005 12:13 PM

I disagree with Bob. It doesn't matter if the household contained more family members - grandparents, cousins, etc. Grammatically speaking, the antecedent to the pronoun "them" can only be the aforementioned of the previous statement, namely Abigail and the children. So Della is right.

Posted by: sw at January 21, 2005 12:40 PM

So were the other half... All 13 were females so that in the end... it's immaterial...

Posted by: |mr|Darcy at January 21, 2005 1:40 PM

Just thinking about the odds of 13 females...

Using the following equation:

nCf = N!/f!(N-f)!

where: nCf is the probability that of x females being born in x births, and

N is the total number of births, and

f is the number of females born

This means that the probability of giving birth to 13 females in 13 births is 0.00000016% or 1 out of every 6,227,020,800 mothers could accomplish this... Very impressive for the mom that does, and my kudos to her - along with a year long vacation to the tiny island nation of Pago Pago to recover...

Well, there are results that DO anchor the ends of the bell curve... And such is this...

Posted by: |mr|Darcy at January 21, 2005 2:26 PM

Here's my first theory... when she had her thirteenth child, her oldest child was 19. Because it was in the early 18th century, that child would be considered an adult, ie. a WOMAN (not a girl). So if she had 7 female and six male children, six of those would be girls.

Posted by: jpr at January 21, 2005 2:39 PM

Mon Dieu! Occam's (or Ockham) Razor... the Principle of Parsimony... the simplest of two competing theories is the preferred... All 13 children were female; there's no word play here. Divide 13 females by two... and the remainder is still all females... Wink, wink, nudge, nudge, say no more, say no more...

|mr|Darcy begins to see why conspiracy theories arise - an absence of practitioners in the truth becuase its too simple to be true...

"Things that make you go Hmmm!"

Posted by: |mr|Darcy at January 21, 2005 2:53 PM

Bob here,

The "them" clearly relates to the children, it's only in attempting to solve a riddle/puzzle that we contemplate "them" relating to Abigail. But who is Abigail, but Mrs. Abigail, a wife, a couple.

Of course, you're clearly right as to the author's intentions. However, the only reason all would not figure it out is that the author intentionally misleads us with bad grammar.

I just don't think that is fair gamesmanship, but that's probably cause I did not figure it out. So, I doing my best to invalidate the puzzle. I'm a Gore voter after all.

Posted by: Bob at January 21, 2005 2:56 PM

Invalidate, indeed! Well, here I must respond because as stated in Newtown's Third Law of Motion, "For every action, there is an equal and opposite reaction."

And thus we see the "harsh", cold logic of a Rebulican with |mr|Darcy's response... Welcome back, Dubya!

Posted by: |mr|Darcy at January 21, 2005 3:07 PM

Ok the poster up top (Della) was right...

However to infer that there was a Mr. such and such...one only gets in trouble by bringing up such assumptions.

What if...Mrs. Eischrank was of the oldest profession in the world? or her husband had recently passed away...or what have you…

I think factoring a husband in to the equation is a poor attempt to avoid the fact that someone got the answer before you did and thus you question the question or even the logic of the question.

Don't mind me...I have a cold. (stupid heated seats)

Posted by: me of me inc. at January 21, 2005 4:27 PM

Wow. You should post more of them, how are they in general?

I don't think this one has been solved, though. I don't know. If that is the answer I would feel cheated.

No offense to my mother Della.

Posted by: Chelsea at January 22, 2005 1:11 PM

The other half were girls as well...

Posted by: Queen of Prussia at January 22, 2005 6:18 PM

"In the early 18th century Mrs. Abigail Eischrank of Cambridge, MA, gave birth to thirteen children. Exactly half of them were girls. Explain."

Mrs. Eischrank, being a woman of childbearing age in the 1700s, would probably object to being referred to as a "girl". As such, I believe the meaning of "them" as previously debated is clearly referring to the 13 children she gave birth to. To include Mrs. Eischrank in the whole would be arguable if the term "girls" was replaced by "female".

At any rate, I am not a mensa candidate. But the most logical answer to the question is that all of the children were girls, probability withstanding. In this manner both halves of the whole would be exacly half female.

Posted by: morgan at January 24, 2005 11:40 AM

The "other half" were girls, too.

She had all girls.

Posted by: Kersten at January 25, 2005 8:37 PM

To say that "them" includes the mother, first of all, while providing a convenient way out, makes the statement itself ambiguous. I demand more information.

Also, left out was whether a Father was included, or for that matter how many fathers were included. Women were known to have two or more husbands then. You know, they died and stuff.

On second thought this doesn't matter, as long as there were an odd number of fathers -- again, not enough information is provided in the given statement.

I like the answer that one of them was a woman by the time the thirteenth girl was born, but that implies a certain age, which again is not provided in the information. I believe in 18th century USA, 18 was the age of adulthood.

Posted by: martianpackets at January 28, 2005 12:29 AM

And we wonder why conspiracy theories abound...

As Arnold said in Kindergarten Cop, "It's not a tumuah!"

I can't help but chuckle... My apologies!

Posted by: |mr|Darcy at January 28, 2005 10:11 AM

And we wonder why conspiracy theories abound...

As Arnold said in Kindergarten Cop, "It's not a tumuah!"

I can't help but chuckle... My apologies!

Posted by: |mr|Darcy at January 28, 2005 10:13 AM

Hey - look above! I'm in stereo ignorance; how'd that happen?!?

Posted by: |mr|Darcy at January 28, 2005 10:15 AM

This is simple. She gave birth to 14 children. Half of them were girls. Just because it says she gave birth to 13 doesnt mean that there isn't a fourteenth.

oh and I have a crush on you now...nice pic, and brains!


Posted by: Greg at February 13, 2005 11:58 PM
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