So how old is Anne?

[mmcirvin]

So recently this made the rounds (via someone on my friends list whose identity I have forgotten):

How old is Anne?

Reportedly this question inspired an ongoing national debate when it appeared in the New York Press in 1903:

Brooklyn, October 12

Dear Tip:

Mary is 24 years old. She is twice as old as Anne was when she was as old as Anne is now. How old is Anne now? A says the answer is 16; B says 12. Which is correct?

John Mahon

I get a third answer. Perhaps it's time for another debate.

As printed (and as I think a commenter said on the LJ where I saw it), it can be interpreted as a stupid trick question about pronoun antecedents. If you work this out with algebra and assume that both instances of the "she" refer to Mary, you find pretty quickly that neither of the provided answers is correct. So if one of the answers is correct (as implied by "Which is correct?") then the second "she" must instead refer to Anne, and "as old as Anne was when Anne was as old as Anne is now" just means "as old as Anne is now" implying that Anne is 12. (But can we use the past tense "was" to refer to the present? And so on and so on...)

If this is, verbatim, how the problem was printed in the New York Press, the absence of a correct answer for the most common interpretation, and the ensuing grammatical gotcha, are probably why it led to a national controversy. So far, so stupid. The interesting thing is that, online, you can also find corrected versions of the problem that just turn it into a simple algebra problem:

So they come to the door tonight asking for a trick or a treat & obviously I give them a trick. (I posted this last year & two people handily answered it right. This is for them what didn't see it then.)

Mary is 24.

She is twice as old
as Ann was when
Mary was as old as
Ann is now.

How old is Ann?


On October 16, 1903, The New York Press published this little word problem. It's dead easy, but the trick part is that it looks easier than it is.

The whole of north America knew of it in a few weeks & for decades later, the phrase "How old is Ann?" came to mean - "Yeah! And you've asked a ridiculously impossible question!" (As it were.)

Would it have really been so controversial in that form? Maybe, but I doubt it. It actually has an unambiguous solution.

This kind of post-hoc correction of trick riddles and shaggy-dog stories (if that's indeed what happened here) goes on a lot, but sometimes it works in the other direction, such as the "third common word that ends in -gry" riddle that (most likely) spontaneously transformed from a dumb but solvable trick question into an impossible puzzle with no real answer.

Comments

[piehead.livejournal.com]

Stupid words, getting in the way of cold, hard logic.

The plot thickens

[mmcirvin.livejournal.com]

The New York Times printed the puzzle on October 9, 1903, in an article implying that it was already a popular stumper by then--and their version is the "corrected" version which reduces to an unambiguous algebra problem. So maybe the mutation went the other way!

Implying?

[notr.livejournal.com]

Stating: "From The World of Yesterday."

[schwa242.livejournal.com]

I think I have it, though I don't know if you want a spoiler typed or not.

[mmcirvin.livejournal.com]

YOU KNOW THE THIRD WORD ENDING IN -GRY????

[mmcirvin.livejournal.com]

...Seriously, go ahead and post it if you like--we're already behind the LJ-cut here.

[schwa242.livejournal.com]

I'm guessing that Anne is 18. When Mary was 18, Anne was 12. Now that Mary is 24, Mary is twice as old as Anne was when Anne was 12 and Mary was 18.

[mmcirvin.livejournal.com]

Right, that's the solution to the problem in its non-broken form.

[mmcirvin.livejournal.com]

Here's a Time magazine letters column from 1952 (http://www.time.com/time/magazine/article/0,9171,857101-3,00.html) that also mentions a more elaborate version by the great puzzle master Sam Loyd (http://en.wikipedia.org/wiki/Sam_Loyd). I suspect it is not the "original" but a parodic variant, but I could be wrong about that too.

[eb-oesch.livejournal.com]

The answer is clearly twenty-nine.

Ann is 29.
Mary is 24.

Ann was 12 when Mary was Ann's current age, 29.

5 years have passed since then in Mary's timeframe. 17 years have passed in Ann's timeframe. It all checks out.

The problem would be ambiguous if Mary and Ann's inertial frames were different at either the start or end of the period in question. The puzzle is clearly meant to be unambiguous, so we can eliminate that possibility, and it's most natural to assume that Mary took a round-trip rocket trip. Assuming that Mary's rocket exerted a constant gravity during her trip out and back, which well-known star was Mary visiting during her trip? Show all your work.

Actually I have no idea how far she traveled, since I never got as far as general relativity, but if you try to fake it, I still might notice. It'll be easier for everyone if you just answer the question correctly.

By the way, I arrived at the correct answer to the original puzzle (29) through a flash of insight. The calculations were just filling in the details. Take that, bitches!

I still don't have my rocketship and household robot, though. Ok, I could buy a Roomba.

But! Sucky work still sucks, and the whole work complex thing with the cubicles and the Office Space doesn't belong in the future I signed up for. Maybe somebody mislaid my application? It's the one with the photo of the Star Trek blue lady stapled to the cover.

Also, nobody warned me that many of the Prisoner episodes would turn out seeming as slapdash, with twist endings bought from a vending machine, as they apparently really were. Also also, I think Patrick McGoohan earns extra Shatner points for having an exec producer role or whatever in the series, because it makes it so easy to imagine McGoohan scribbling "thinks I'm damned sexy" into all the female character descriptions.