Logic Puzzle #3

[The Armchair]

You're sitting at the 2/6 table at the Excal. You, being a cordial 2+2er, know to answer logic puzzles in white-on-white text, as to not give it away for your fellow boardmates. A seat opens on your left, and a guy you've never seen before sits down. (We'll call him "Left.") But the guy on your right ("Right") does know him -- they were former college roommates!

Putting collusion issues aside (the guy on the right is a total fish), you stay at the table.

And then the strangest conversation happens:

Left: Hey, Right, how's it goin! Long time no see!
Right: Hey! How's by you?
Left: Good, good... on vacation with the fam. Wife's upstairs with the three kids.
Right: Three? Wow, congrats, how old are they?
Left: I'm not going to tell you.
Right: ???

At this point, you're struggling mightily to figure out how Right successfully said "???," given the lack of vowels. But no matter -- the conversation just got interesting.

Left: I'm sure you can figure it out.
Right: Uh. . . how.
Left: I'll give you clues, of course.
Right: Of course.

(Apparently, they used to do this all the time. It's amazingly that either of them ever got far enough into a relationship to have children.)

Left: Multiple their ages together and you'll get 36, then --
Right: Okay, so, they're . . . wait a sec, I can't figure it out yet!
Left: Maybe you shouldn't interrupt, then? In any event, you're right, you can't figure it out yet. You also need to know that if you add their ages together, it equal our old dorm room mumber.
Right: Hey, neato. So they're . . . wait, I also need to know --
Left: The oldest one can read.
Right: Cool. Thanks.

At this point, you're confused. Left, always looking to screw with someone, turns to you and says:

Left: I'll pay your next three blinds if you can tell me how old my kids are. Five if you can tell me how you figured it out.

You answer. . . ?

(Edit in italics)

[aloiz]

Ok I'll post in whit this time.
<font color="white">
The last question asked I deduced to be whether the twins were older or younger than the third child. Given that the answer was older the only combination is 6,6,1.
</font>

aloiz

[The Armchair]

Given what I wrote, you're right, but I changed it to make it so you're wrong. The reason I changed it is because your reasoning is incomplete due to an omission on my part.

[AndysDaddy]

My response in White:
<font color="white"> The answer is 6, 6, and 1. The only way that the unanswered (to us) dorm room question could ellicit right's response is if two such sums added up equally. The combos of 6x6x1 and 2x2x9 both add up to 13. The unasked question was "Are the twins younger or older than their sibling". Since they are older, the answer must be 6,6, and 1.</font>

[The Armchair]

Five blinds to you. Perfect answer (at least before my edit).

[AndysDaddy]

Your edit does not change my answer, and changes the reasoning only superficially. In fact, your change seems to make the answer ambiguous. More in white:
<font color="white">Six year olds can certainly be expected to be able to read, if only a bit, as can nine year olds. While your statment "The oldest can read" (my emphasis) implies that the oldest is not a twin, in fact one of the twins is older (as any older twin will probably tell you).</font>
So now I am confused as to what the correct reasoning is.

[aloiz]

Now I'm slightly confused. Before you've changed it I don't see how my reasoning is incomplete given what you wrote. Now given what you've added I'm slightly less sure of the answer. Here's what I got:
<font color="white">
All three number combinations that multiply up to 36:
6 6 1
9 2 2
2 3 6
4 3 3
36 1 1
9 4 1
12 3 1
18 2 1
Only two of those combinations add up to the same number (661 and 922), and since we know that the dorm room number was insufficient information these are the only two possiblities. The oldest one can read I assume that means 9 2 2, but plenty of kids read at age 6, and one twin is always older than the other so I'm not exactly sure. Maybe I'm missing something.
</font>


aloiz

[The Armchair]

<font color="white"> (a) If it's enough information for the roommate, then it cannot create ambiguity. Even though one twin is technically older than the other, that's clearly irrelevant. </font>

[kyro]

i didn't look at the answers, so therefore no chance of me stealing anyone's glory...

my guess is 2,2,9

Right couldn't tell the ages of the kids even after Left told him the sum was their dorm number. So of the 8 possibly ways to factor, only two make sense, as they are the only two combinations that have the same sum.

1,6,6
2,2,9

My final guess is really a leap of faith. Left says "oldest child" which suggests one child can be the oldest. Since the first combination has two "oldest children" the second combination seems to be the only possible answer.

How'd I do? <font color="white"> </font>

[jwvdcw]

<font color="white">I guess I"m totally retarded, but where does it say that theres twins? It seems as if everyone is getting this from the 'add their ages equals our dorm room number, but I just don't get it. 6+6+1= 13..what does that tell you?</font>