Logic Puzzle #3

[aloiz]

Response in white:
<font color="white">
There's only two three number combinations that multiply to 36 and add up to the same number, 922 and 661. Since the dorm room number was not enough information we know that these are the only two possibilities. Armchair changed his original post, which originally had the response to the last question as "yes they're older" in which case you assume the unasked question was refering to the twins being older or younger than the third child. Now that he changed it to "yes the oldest can read" I think there's more ambiguity in the question than before. However using the last clue you're suppose to eliminate the 661 as a possiblity. </font>

aloiz

[jdl22]

<font color="white"> Just thinking out loud through this. So the product of the three is 36. Numbers that multiplied together equal 36 are 36x1,18x2,12x3,9x4,6x6

That leaves these possible combinations (with sum after):
1,1,36 - 38
2,1,18 - 21
2,2,9 - 13
2,3,6 - 11
3,1,12 - 16
3,3,4 - 10
4,1,9 - 14
4,3,3 - 10
6,1,6 - 13
6,2,3 - 11

There are some duplicates here so the shortened list is:
1,1,36 - 38
1,2,18 - 21
1,3,12 - 16
1,4,9 - 14
1,6,6 - 13
2,2,9 - 13
2,3,6 - 11
3,3,4 - 10

Since the guy had to qualify his statement that must mean that there are two possibilities for solutions to the problem, ie two possible 3 number sets that add up to their dorm room number whose product is 36. That could only mean that their dorm room number is 13. Hence the children are either two, two, and nine or one, six, and six. At this point we have a problem. Nine year olds and six year olds can read. If he considers people with the same number of years as the same age then clearly they are 2, 2, and 9. If not then it could be either.</font>

[jwvdcw]

Ok I get how you get down to 2 possibilites now....but the 'the older one can read' still makes no sense to me since 1.theres twins and 2.Can't 6 year olds and 9 year olds read?

[The Armchair]

It's a nitpick, but an entirely fair one. Of course, it's also a requiste part of the question that we're treating the kids' ages as integers; therefore, there's no difference between 6 and 6. The answer must be 9, 2, 2.

If you want to claim ambiguity, that's fine, but you should either treat the kids as integers or not, and not mix-match.

In any event, the ambiguity is my fault. The original italicized line said "They're older," which is fine, but it guts the question. That's a not-so-clear reference to the existance of twins, and the only set of twins older than the third child is 6, 6, 1. I should have said "they're younger," which would have made the options 36,1,1 9,2,2 and 4,3,3. That'd require the full analysis.

[GuyOnTilt]

Booooo! Something hard please!!!

GoT