What ARE the ages of the girl's brothers?
March 23, 2011 7:18 AM Subscribe
Can you help me solve this puzzle, which appeared in the problem solving section of my university's scholarship exam for first-year students?
The other questions in that section tend to be straightforward mathematical reasoning puzzles, along the lines of "You have a seven ounce container and a four ounce container - describe how you can use them to dole out one, two, three, five and six ounces of sugar". Frankly, I am rubbish enough at those as it is. I didn't even know where to start with this one, which goes as follows:
Two teenagers, a boy and a girl, are out on their first date. After seeing a movie, they end up at a hamburger restaurant. Both are rather shy, and don't know what to talk about. Eventually, the boy breaks the silence, and the ensuing conversation goes like this:
He: "Do you have any brothers?"
She: "Yes, three."
He: "What are their ages?"
She: "I hear that you are good at arithmetic. So, I'll give you that information in the form of a puzzle: Their ages (all whole numbers), when multiplied together, are equal to the age of my grandmother, who is seventy-two.
The boy does some calculations on a paper napkin.
He: "That doesn't give me enough information."
She: "Their ages, when added together, are equal to the number of tables in this restaurant."
The boy does some more calculations on the napkin, and then looks around.
He: "I've counted the tables, but still can't tell their ages."
She: "I'll give you one last clue: The name of my youngest brother is Jimmy."
He says: "Aha", and gives her the correct ages of her brothers.
What are the ages of the girl's brothers?
The other questions in that section tend to be straightforward mathematical reasoning puzzles, along the lines of "You have a seven ounce container and a four ounce container - describe how you can use them to dole out one, two, three, five and six ounces of sugar". Frankly, I am rubbish enough at those as it is. I didn't even know where to start with this one, which goes as follows:
Two teenagers, a boy and a girl, are out on their first date. After seeing a movie, they end up at a hamburger restaurant. Both are rather shy, and don't know what to talk about. Eventually, the boy breaks the silence, and the ensuing conversation goes like this:
He: "Do you have any brothers?"
She: "Yes, three."
He: "What are their ages?"
She: "I hear that you are good at arithmetic. So, I'll give you that information in the form of a puzzle: Their ages (all whole numbers), when multiplied together, are equal to the age of my grandmother, who is seventy-two.
The boy does some calculations on a paper napkin.
He: "That doesn't give me enough information."
She: "Their ages, when added together, are equal to the number of tables in this restaurant."
The boy does some more calculations on the napkin, and then looks around.
He: "I've counted the tables, but still can't tell their ages."
She: "I'll give you one last clue: The name of my youngest brother is Jimmy."
He says: "Aha", and gives her the correct ages of her brothers.
What are the ages of the girl's brothers?
or 1, 8, and 9...
posted by -->NMN.80.418 at 7:25 AM on March 23, 2011
posted by -->NMN.80.418 at 7:25 AM on March 23, 2011
Ok, but how did you get that? And how did the name of the youngest brother help any?
posted by theichibun at 7:26 AM on March 23, 2011
posted by theichibun at 7:26 AM on March 23, 2011
To quote my second grade math teacher: "Show your work, jannw!"
posted by Grither at 7:26 AM on March 23, 2011
posted by Grither at 7:26 AM on March 23, 2011
The youngest brother helps because 3 3 9 otherwise works but then their isn't a 'youngest' brother.
posted by Confess, Fletch at 7:28 AM on March 23, 2011
posted by Confess, Fletch at 7:28 AM on March 23, 2011
meh ... other option of 3,3 and 8 is not possible as the existence of a younger brother rules out twins.
posted by jannw at 7:28 AM on March 23, 2011
posted by jannw at 7:28 AM on March 23, 2011
Don't we need the number of tables? Or am I missing something?
posted by Grither at 7:30 AM on March 23, 2011
posted by Grither at 7:30 AM on March 23, 2011
Correct me if I'm wrong, but it's my understanding that twins are rarely if ever born at exactly the same time, and there are plenty of examples of one twin asserting that they're five minutes older or whatever.
And correct me if I'm wrong, but it seems like it's also fairly common for siblings by marriage, adoption, fostering, etc. to simply refer to themselves as brothers and sisters.
posted by box at 7:31 AM on March 23, 2011 [2 favorites]
And correct me if I'm wrong, but it seems like it's also fairly common for siblings by marriage, adoption, fostering, etc. to simply refer to themselves as brothers and sisters.
posted by box at 7:31 AM on March 23, 2011 [2 favorites]
The question didn't give the number of tables then? If the question did give the number of tables (as 15) then it would be because the two options are 2,4,9 or 3,3,9 - if she has a youngest brother than the answer must be 2,4,9
posted by missmagenta at 7:31 AM on March 23, 2011
posted by missmagenta at 7:31 AM on March 23, 2011
two or three cars: is this the exact wording of the puzzle as it appears on the exam?
posted by box at 7:32 AM on March 23, 2011
posted by box at 7:32 AM on March 23, 2011
Just a thought. "Youngest brother" indicates she is older than at least two of them. Let's say her brothers are XYZ and she is S.
So the birth order could be SXYZ or XSYZ. (On preview: I don't think this rules out twins altogether--just rules out twins if she has an older brother.)
But--conventionally--don't people usually refer to twins as being the same age? Like if I had twin siblings I wouldn't say that one is 'younger' or 'older' than the other.
posted by methroach at 7:33 AM on March 23, 2011
So the birth order could be SXYZ or XSYZ. (On preview: I don't think this rules out twins altogether--just rules out twins if she has an older brother.)
But--conventionally--don't people usually refer to twins as being the same age? Like if I had twin siblings I wouldn't say that one is 'younger' or 'older' than the other.
posted by methroach at 7:33 AM on March 23, 2011
Best answer: We don't need to know the number of tables.
The reason the number of tables is important is that we know that the sum of the ages doesn't give him enough information to solve the puzzle. So there must be two possible solutions that add to the same number.
My quick calculations show those as 2, 6, 6 or 3, 3, 8 (both add to 14).
The fact that there is a "youngest" brother meanas that the answer must be 2, 6, 6.
posted by cider at 7:33 AM on March 23, 2011 [13 favorites]
The reason the number of tables is important is that we know that the sum of the ages doesn't give him enough information to solve the puzzle. So there must be two possible solutions that add to the same number.
My quick calculations show those as 2, 6, 6 or 3, 3, 8 (both add to 14).
The fact that there is a "youngest" brother meanas that the answer must be 2, 6, 6.
posted by cider at 7:33 AM on March 23, 2011 [13 favorites]
The problem is best tackled by factoring 72 into 3 * 3 * 2 * 2 * 2 * 1.
This leaves the sets of three ages as 9, 4, and 2 (if we ignore 1 as a factor) or 9, 8, and 1 (if we include 1 as a factor). The knowledge that there is a single youngest rules out the possibility that there is an 18-year-old with two twin 2-year-olds.
missmagenta, 3, 3, 9 makes 81, not 72
posted by -->NMN.80.418 at 7:35 AM on March 23, 2011
This leaves the sets of three ages as 9, 4, and 2 (if we ignore 1 as a factor) or 9, 8, and 1 (if we include 1 as a factor). The knowledge that there is a single youngest rules out the possibility that there is an 18-year-old with two twin 2-year-olds.
missmagenta, 3, 3, 9 makes 81, not 72
posted by -->NMN.80.418 at 7:35 AM on March 23, 2011
Best answer: First clue: The prime factors of 72 are (1,2,2,2,3,3), so the ages must be some combination of these factors.
Second clue: We know that there are two combinations of these factors that add up to the same number. This rules out (2,4,9),(1,8,9),(3,4,6), etc - (3,3,8) and (2,6,6) both add up to 14
Third clue: Since there is a younger brother (ruling out twins), I'm saying the answer is (2,6,6)
I haven't worked out every permutation, but this is the first one that fits all three clues.
posted by muddgirl at 7:35 AM on March 23, 2011 [3 favorites]
Second clue: We know that there are two combinations of these factors that add up to the same number. This rules out (2,4,9),(1,8,9),(3,4,6), etc - (3,3,8) and (2,6,6) both add up to 14
Third clue: Since there is a younger brother (ruling out twins), I'm saying the answer is (2,6,6)
I haven't worked out every permutation, but this is the first one that fits all three clues.
posted by muddgirl at 7:35 AM on March 23, 2011 [3 favorites]
In other words, I agree with Cider and I think everyone else so far has ignored one clue or another.
posted by muddgirl at 7:37 AM on March 23, 2011
posted by muddgirl at 7:37 AM on March 23, 2011
box: this is clearly one of those problems that requires deeply narrow, technical, and lawyerly readings of its internal rules.
The brothers all have ages in whole numbers. OBVIOUSLY*, this doesn't mean that the ages being reported to you are whole-number approximations of their ages; instead, it means that at the microsecond that the statement is being given, all of the children have ages that are literally exact whole numbers: for someone to be 9 in this puzzle means that they are exactly 9, not a Planck-instant older or younger.
By interpreting the question in this way, it rules out twins -- if there were twins, it would be impossible for the brothers' ages to all be the literal, exact whole numbers that the sister stated.
*You're right, this isn't obvious at all, and is in direct contradiction to normal English usage of ages.
posted by ROU_Xenophobe at 7:37 AM on March 23, 2011 [1 favorite]
The brothers all have ages in whole numbers. OBVIOUSLY*, this doesn't mean that the ages being reported to you are whole-number approximations of their ages; instead, it means that at the microsecond that the statement is being given, all of the children have ages that are literally exact whole numbers: for someone to be 9 in this puzzle means that they are exactly 9, not a Planck-instant older or younger.
By interpreting the question in this way, it rules out twins -- if there were twins, it would be impossible for the brothers' ages to all be the literal, exact whole numbers that the sister stated.
*You're right, this isn't obvious at all, and is in direct contradiction to normal English usage of ages.
posted by ROU_Xenophobe at 7:37 AM on March 23, 2011 [1 favorite]
A bit more explanation:
The way I did it was through brute force: I factored 72 = 1 x 2 x 2 x 2 x 3 x 3, and then figured out all the possible ages.
So, 72 = 1 x 1 x 72
or 72 = 1 x 2 x 36
...
or 72 = 2 x 2 x 18
or 72 = 2 x 4 x 9
....
or 72 = 3 x 3 x 8
or 72 = 3 x 4 x 6
I then added them all together. The only two combinations that added up to the same number were 2, 6, 6, or 3, 3, 8.
posted by cider at 7:37 AM on March 23, 2011
The way I did it was through brute force: I factored 72 = 1 x 2 x 2 x 2 x 3 x 3, and then figured out all the possible ages.
So, 72 = 1 x 1 x 72
or 72 = 1 x 2 x 36
...
or 72 = 2 x 2 x 18
or 72 = 2 x 4 x 9
....
or 72 = 3 x 3 x 8
or 72 = 3 x 4 x 6
I then added them all together. The only two combinations that added up to the same number were 2, 6, 6, or 3, 3, 8.
posted by cider at 7:37 AM on March 23, 2011
Also, I should say: "The second clue tells us that there are at least two combinations of factors that add up to the same number." I just found two and one of them fit all the clues, but there may be more.
posted by muddgirl at 7:38 AM on March 23, 2011
posted by muddgirl at 7:38 AM on March 23, 2011
Response by poster: Well, it appears that cider and muddgirl have it. God, Metafilter is so smart! Thank you for your help, everyone.
(box - yes, I typed it exactly as it was, down to the missing closing quotation mark after "seventy-two.")
posted by two or three cars parked under the stars at 7:40 AM on March 23, 2011 [3 favorites]
(box - yes, I typed it exactly as it was, down to the missing closing quotation mark after "seventy-two.")
posted by two or three cars parked under the stars at 7:40 AM on March 23, 2011 [3 favorites]
I still argue that the wording doesn't rule out twins entering the picture. Every set of twins I've know made a big deal about which one was older. Or at least the older one did.
posted by theichibun at 7:42 AM on March 23, 2011 [1 favorite]
posted by theichibun at 7:42 AM on March 23, 2011 [1 favorite]
The wording doesn't rule out adopted brothers either. They are all adopted brothers with the same birthday, and the older "twins" were born at the exact same second.
If clue 3 isn't a discriminator between potential answers, then there is no right answer and it's a terrible puzzle. Therefore, it is a discriminating answer and we can rule out either (2,6,6) or (3,3,8)
posted by muddgirl at 7:44 AM on March 23, 2011
If clue 3 isn't a discriminator between potential answers, then there is no right answer and it's a terrible puzzle. Therefore, it is a discriminating answer and we can rule out either (2,6,6) or (3,3,8)
posted by muddgirl at 7:44 AM on March 23, 2011
Detailed solution of the intended answer:
Here's all possible combinations of three integers whose product is 72, along with the sum of those integers:
1x1x72 [74]
1x2x36 [39]
1x3x24 [28]
1x4x18 [23]
1x6x12 [19]
1x8x9 [18]
2x2x18 [22]
2x3x12 [17]
2x4x9 [15]
2x6x6 [14]
3x3x8 [14]
3x4x6 [13]
So if there had been 74, 39, 28, 23, 19, 18, 22, 17, 15, or 13 tables in the restaurant, "He" would have had enough information to determine the ages of "Her" siblings after counting those tables. The only case in which the ages are still ambiguous after counting tables are if there are 14 tables. Then "He" does not know if "Her" siblings are 2,6,6 or 3,3,8.
The "youngest brother" clue is supposed to indicate that the youngest is not a twin, and expected to rule out the 3,3,8 combination. I object to this because a) as box points out, even among twins one is minutes or sometimes hours older than the other; b) siblings which are the same "age" are not necessarily twins; one may be 3 years 11 months, and the other 3 years 0 months, and both would commonly said to be "3 years old," while the latter would still be said to be the "youngest sibling."
posted by DevilsAdvocate at 7:48 AM on March 23, 2011 [1 favorite]
Here's all possible combinations of three integers whose product is 72, along with the sum of those integers:
1x1x72 [74]
1x2x36 [39]
1x3x24 [28]
1x4x18 [23]
1x6x12 [19]
1x8x9 [18]
2x2x18 [22]
2x3x12 [17]
2x4x9 [15]
2x6x6 [14]
3x3x8 [14]
3x4x6 [13]
So if there had been 74, 39, 28, 23, 19, 18, 22, 17, 15, or 13 tables in the restaurant, "He" would have had enough information to determine the ages of "Her" siblings after counting those tables. The only case in which the ages are still ambiguous after counting tables are if there are 14 tables. Then "He" does not know if "Her" siblings are 2,6,6 or 3,3,8.
The "youngest brother" clue is supposed to indicate that the youngest is not a twin, and expected to rule out the 3,3,8 combination. I object to this because a) as box points out, even among twins one is minutes or sometimes hours older than the other; b) siblings which are the same "age" are not necessarily twins; one may be 3 years 11 months, and the other 3 years 0 months, and both would commonly said to be "3 years old," while the latter would still be said to be the "youngest sibling."
posted by DevilsAdvocate at 7:48 AM on March 23, 2011 [1 favorite]
But doesn't the point that the ages are all whole numbers, ie integers, constrain every two-year-old in this scenario to being precisely two years old, every five-year-old to being precisely five years old, etc?
posted by oliverburkeman at 7:52 AM on March 23, 2011
posted by oliverburkeman at 7:52 AM on March 23, 2011
The correct question for this puzzle, after the same setup, is "how many tables are in the restaurant."
posted by rokusan at 7:57 AM on March 23, 2011 [3 favorites]
posted by rokusan at 7:57 AM on March 23, 2011 [3 favorites]
It's definitely possible to have siblings who are the same age, but not twins, where one is clearly older than the other. For example, if they were born 11 months apart, there will be a one-month window every year where they're the same age.
posted by Doofus Magoo at 7:58 AM on March 23, 2011
posted by Doofus Magoo at 7:58 AM on March 23, 2011
I object to the idea that if Jimmy is the "youngest" then no one is the same numerical age as him. Jimmy and the next-youngest brother could be the same age, even if there are no twins, and even if "brother" just means biological brother. Some children who are biologically born of the same parents are sometimes the same age. They're just born less than 365 days apart because the parents conceived the younger one shortly after the older one was born. This is not some far-fetched hypothetical -- I have a friend who's 11 months older than her sister.
posted by John Cohen at 8:01 AM on March 23, 2011
posted by John Cohen at 8:01 AM on March 23, 2011
Doofus Magoo: For example, if they were born 11 months apart, there will be a one-month window every year where they're the same age
Sure. This was true for my sister and I. So the question is flawed in its premise. But having said that, if we go with rokusan's twist:
The correct question for this puzzle, after the same setup, is "how many tables are in the restaurant."
...I still think it is a neat and satisfying little puzzle.
posted by DarlingBri at 8:03 AM on March 23, 2011
Sure. This was true for my sister and I. So the question is flawed in its premise. But having said that, if we go with rokusan's twist:
The correct question for this puzzle, after the same setup, is "how many tables are in the restaurant."
...I still think it is a neat and satisfying little puzzle.
posted by DarlingBri at 8:03 AM on March 23, 2011
Again, we are thinking in real-world-logic, not puzzle logic. If Clue #3 didn't discriminate between potential answers, then Girlfriend would not have presented it as a clue. Since it was presented, then it does discriminate between answers, and we can assume that her brothers are all adopted, or that the twins consider themselves to be exactly the same age, and that they are all at least 1 year apart, etc. etc.
posted by muddgirl at 8:14 AM on March 23, 2011 [2 favorites]
posted by muddgirl at 8:14 AM on March 23, 2011 [2 favorites]
Of course, the correct answer for this is "It doesn't matter how many brothers she has because anyone who would present me with a puzzle like this instead of just answering the damn question is getting dumped right there."
The whole number argument also doesn't really say that all 2 year olds are exactly 2. It just says that we're working with a data set that doesn't involve the use of fractions or decimals.
two or three cars parked under the stars, would it be possible for you to go ask what the correct answer is? I'm sure it's what you have marked as a best answer. But as someone who went through stats a research methods with two professors who made us rip our surveys apart to find even the smallest most insignificant problem in the way questions are construed, I have a huge issue with the logic here.
posted by theichibun at 8:23 AM on March 23, 2011
The whole number argument also doesn't really say that all 2 year olds are exactly 2. It just says that we're working with a data set that doesn't involve the use of fractions or decimals.
two or three cars parked under the stars, would it be possible for you to go ask what the correct answer is? I'm sure it's what you have marked as a best answer. But as someone who went through stats a research methods with two professors who made us rip our surveys apart to find even the smallest most insignificant problem in the way questions are construed, I have a huge issue with the logic here.
posted by theichibun at 8:23 AM on March 23, 2011
If Clue #3 didn't discriminate between potential answers, then Girlfriend would not have presented it as a clue. Since it was presented, then it does discriminate between answers, and we can assume that her brothers are all adopted, or that the twins consider themselves to be exactly the same age, and that they are all at least 1 year apart, etc. etc.
I disagree. Puzzles often include red herrings. Part of the challenge is to sort out the red herrings from crucial clues. If the puzzle inherently prevents the solver from doing this based on a combination of logic and background knowledge, that's a defect with the puzzle. The solver has enough trouble just figuring the thing out; the burden is on the puzzle creator to make a puzzle that can be figured out, especially on an important exam.
posted by John Cohen at 8:46 AM on March 23, 2011
I disagree. Puzzles often include red herrings. Part of the challenge is to sort out the red herrings from crucial clues. If the puzzle inherently prevents the solver from doing this based on a combination of logic and background knowledge, that's a defect with the puzzle. The solver has enough trouble just figuring the thing out; the burden is on the puzzle creator to make a puzzle that can be figured out, especially on an important exam.
posted by John Cohen at 8:46 AM on March 23, 2011
Response by poster: theichibun: I'll ask around, but my school is so disorganised that I doubt anybody will know what I'm talking about. I'm also not sure who to approach, as the scholarship exam doesn't appear to be administered by any part of the university in particular, and this question is from a while ago. But I'll report back if I get an answer.
posted by two or three cars parked under the stars at 8:52 AM on March 23, 2011
posted by two or three cars parked under the stars at 8:52 AM on March 23, 2011
I did these sorts of logic puzzles in high school, and yes you need to not overthink some of the details and accept things literally... or the "puzzle logic" as stated. This is an old puzzle, to be sure.
I recall one puzzle involving calculating the area that a hour hand on a clock covers in a given amount of time. I argued that it was unanswerable because we didnt know the lengths of the hands... I was told to stfu and do the question, pretending that all hands extend to the edge of the clock.
Bean plating these puzzles does not help you on math tests...
posted by utsutsu at 8:58 AM on March 23, 2011
I recall one puzzle involving calculating the area that a hour hand on a clock covers in a given amount of time. I argued that it was unanswerable because we didnt know the lengths of the hands... I was told to stfu and do the question, pretending that all hands extend to the edge of the clock.
Bean plating these puzzles does not help you on math tests...
posted by utsutsu at 8:58 AM on March 23, 2011
And this is why I don't like these puzzles. Too much ignoring of real world knowledge. Everyone knows that the hour hand is shorter than the minute hand in an attempt to make it more clear which one is which. If they're both extending to the edge of the clock then the clock is useless and who cares what the area is since you can't use the thing to tell when that period of time is finished.
posted by theichibun at 9:01 AM on March 23, 2011
posted by theichibun at 9:01 AM on March 23, 2011
I recall one puzzle involving calculating the area that a hour hand on a clock covers in a given amount of time. I argued that it was unanswerable because we didnt know the lengths of the hands... I was told to stfu and do the question, pretending that all hands extend to the edge of the clock.
OK, so that was another flawed puzzle! I'm sure there have been many flawed problems on exams. While that might make for a fascinating Metafilter thread, it's sort of a derail from this specific question.
Notice that if the puzzle is expecting students to rule out adopted brothers, foster children, and born-11-months-apart siblings, it could have cultural/class biases. For instance, students who were adopted will have a harder time going through the mental gymnastics that the question seems to expect of them.
posted by John Cohen at 9:05 AM on March 23, 2011
OK, so that was another flawed puzzle! I'm sure there have been many flawed problems on exams. While that might make for a fascinating Metafilter thread, it's sort of a derail from this specific question.
Notice that if the puzzle is expecting students to rule out adopted brothers, foster children, and born-11-months-apart siblings, it could have cultural/class biases. For instance, students who were adopted will have a harder time going through the mental gymnastics that the question seems to expect of them.
posted by John Cohen at 9:05 AM on March 23, 2011
Puzzles often include red herrings. Part of the challenge is to sort out the red herrings from crucial clues.
Exactly, and in this case Clue #3 was a crucial clue that leads to an answer to the puzzle. Without Clue #3 there is no answer.
I'm not saying it's a good puzzle, but in my experience some nit-picky puzzle solvers will take issue with the wording of any and every puzzle that isn't framed so carefully that it gives the answer away in advance.
posted by muddgirl at 9:09 AM on March 23, 2011
Exactly, and in this case Clue #3 was a crucial clue that leads to an answer to the puzzle. Without Clue #3 there is no answer.
I'm not saying it's a good puzzle, but in my experience some nit-picky puzzle solvers will take issue with the wording of any and every puzzle that isn't framed so carefully that it gives the answer away in advance.
posted by muddgirl at 9:09 AM on March 23, 2011
The whole number argument also doesn't really say that all 2 year olds are exactly 2. It just says that we're working with a data set that doesn't involve the use of fractions or decimals.
It has to say that, though.
If "whole number ages" doesn't mean that the brothers have literal, exact whole number ages, then the use of "youngest" doesn't discriminate between the two possibilities. You could have the youngest three year old, the second-youngest three year old, and the eight year old.
posted by ROU_Xenophobe at 9:41 AM on March 23, 2011
It has to say that, though.
If "whole number ages" doesn't mean that the brothers have literal, exact whole number ages, then the use of "youngest" doesn't discriminate between the two possibilities. You could have the youngest three year old, the second-youngest three year old, and the eight year old.
posted by ROU_Xenophobe at 9:41 AM on March 23, 2011
The problem with nitpicking is that you can always pick further nits. It never stops.
I gave this puzzle to my space alien friend Zondok VII. Zondok concluded that the brother's ages are 3, 6, and 8.
Why?
posted by It's Never Lurgi at 9:42 AM on March 23, 2011
I gave this puzzle to my space alien friend Zondok VII. Zondok concluded that the brother's ages are 3, 6, and 8.
Why?
posted by It's Never Lurgi at 9:42 AM on March 23, 2011
Damnit, I gave away the answer with giving the brother's ages. Crap.
Okay, Zondok concludes that the oldest brother is 8. How about that?
posted by It's Never Lurgi at 9:49 AM on March 23, 2011
Okay, Zondok concludes that the oldest brother is 8. How about that?
posted by It's Never Lurgi at 9:49 AM on March 23, 2011
The twins thing ruins this for me, it's a well known fact that twins often consider one twin to be older than the other. How to reconcile that with the "the ages (all whole numbers)" thing isn't clear, since that could be justifiably interpreted in different ways. A better last clue would have been something like "Phillip and Greg were playing checkers at the hospital when Jimmy was born."
All good puzzlers pick nits, all good puzzles can defend such nitpicking.
posted by skewed at 10:14 AM on March 23, 2011 [1 favorite]
All good puzzlers pick nits, all good puzzles can defend such nitpicking.
posted by skewed at 10:14 AM on March 23, 2011 [1 favorite]
Also, Irish twins. If the two youngest were birn within a year of each other...
posted by seanyboy at 10:19 AM on March 23, 2011
posted by seanyboy at 10:19 AM on March 23, 2011
All good puzzlers pick nits, all good puzzles can defend such nitpicking.
Then what is the correct answer to the puzzle, given that these nits have been picked? Are you saying that the scholarship applicant should write, "there is no solution"?
posted by muddgirl at 10:23 AM on March 23, 2011
Then what is the correct answer to the puzzle, given that these nits have been picked? Are you saying that the scholarship applicant should write, "there is no solution"?
posted by muddgirl at 10:23 AM on March 23, 2011
I was on my high school math team (a long time ago) and after each match, our faculty advisor would appeal any of our wrong answers by picking nits like the above. We were NYC champs most years. Q.E.D.
posted by Obscure Reference at 10:53 AM on March 23, 2011
posted by Obscure Reference at 10:53 AM on March 23, 2011
muddgirl: "Are you saying that the scholarship applicant should write, "there is no solution""
No, they should say that there isn't enough information to solve the problem. There clearly is a solution, but if the answer is 2/6/6 or 3/3/8 isn't able to be known since we don't know if Jimmy is one of the kids that shares an age in this world where we're truncating ages at the decimal point.
Also, this reminds me of when my dad told me that there's no shame in saying that you don't know something in situations like this were you really don't. Saying you need more information to solve a problem was better in his eyes (which watched over Air Force squadrons and have been in charge of numerous groups of people) then having a solution that basically got pulled out of your butt since you didn't have enough information to really solve the problem.
posted by theichibun at 11:59 AM on March 23, 2011
No, they should say that there isn't enough information to solve the problem. There clearly is a solution, but if the answer is 2/6/6 or 3/3/8 isn't able to be known since we don't know if Jimmy is one of the kids that shares an age in this world where we're truncating ages at the decimal point.
Also, this reminds me of when my dad told me that there's no shame in saying that you don't know something in situations like this were you really don't. Saying you need more information to solve a problem was better in his eyes (which watched over Air Force squadrons and have been in charge of numerous groups of people) then having a solution that basically got pulled out of your butt since you didn't have enough information to really solve the problem.
posted by theichibun at 11:59 AM on March 23, 2011
...there's no shame in saying that you don't know something in situations like this were you really don't
And there's clearly no shame in overthinking what was meant to be a simple problem. Also, no scholarship money.
posted by muddgirl at 12:00 PM on March 23, 2011
And there's clearly no shame in overthinking what was meant to be a simple problem. Also, no scholarship money.
posted by muddgirl at 12:00 PM on March 23, 2011
Any school that decides to not give me a scholarship because I give them the correct answer (which in this case is that I can't determine the answer with the information given) to a question like this doesn't deserve to get my tuition money anyway.
I'm really hoping that the answers to this question are looked at more for the thought process and reasoning and less for the actual answer.
If you'd rather have an answer that's actually an answer, then I'd say that it's either 2/2/6 or 3/8/8 but there isn't enough information to make a distinction, especially considering that there has to be a pair of brothers in there that have the same whole number age.
posted by theichibun at 12:09 PM on March 23, 2011 [1 favorite]
I'm really hoping that the answers to this question are looked at more for the thought process and reasoning and less for the actual answer.
If you'd rather have an answer that's actually an answer, then I'd say that it's either 2/2/6 or 3/8/8 but there isn't enough information to make a distinction, especially considering that there has to be a pair of brothers in there that have the same whole number age.
posted by theichibun at 12:09 PM on March 23, 2011 [1 favorite]
There is no doubt in my mind that the solution is knowable and is 2/6/6. For one, the question itself talks about ages as whole numbers so even if the one born last is Jimmy, for the purpose of this question he would be the same age as his twin if he were a twin; he would not be considered youngest. While I can see a valid answer being I don't know it is between 2/6/6 and 3/3/8 and explain your nitpick, I do not think that is in the spirit of the question based on the whole number qualification above.
Cider and muddgirl would get the scholarship money in my opinion.
posted by JohnnyGunn at 12:12 PM on March 23, 2011
Cider and muddgirl would get the scholarship money in my opinion.
posted by JohnnyGunn at 12:12 PM on March 23, 2011
The fact that the girl thinks that the line "The name of my youngest brother is Jimmy." is a clue -- and the fact that the boy successfully uses it to solve the puzzle -- indicates to me that the boy and the girl are both thinking that the two hypothetical brothers in the 3/3/8 solution would be considered the same age, and thus there would be no "youngest".
They might be wrong -- they might not have been thinking about older twins and younger twins as possibilities -- but it's logical to think that that's what's going through their minds, and therefore, it's logical to think that 2/6/6 is the right answer. After all, the puzzle TELLS us that the boy gets the right ages. How could he have done so if there weren't enough information?
If the puzzle weren't filtered through these characters, I feel like you might be able to argue differently. But to me, there's no question in this case.
posted by cider at 12:59 PM on March 23, 2011
They might be wrong -- they might not have been thinking about older twins and younger twins as possibilities -- but it's logical to think that that's what's going through their minds, and therefore, it's logical to think that 2/6/6 is the right answer. After all, the puzzle TELLS us that the boy gets the right ages. How could he have done so if there weren't enough information?
If the puzzle weren't filtered through these characters, I feel like you might be able to argue differently. But to me, there's no question in this case.
posted by cider at 12:59 PM on March 23, 2011
Then what is the correct answer to the puzzle, given that these nits have been picked? Are you saying that the scholarship applicant should write, "there is no solution"?
I guess the correct answer is "there is not enough information to be certain the ages of the children, even though it seems like 2-6-6 is the intended answer." As it is, there are certain assumptions underlying the "correct" answer that are not unambiguously valid. Obviously, if I were to be sitting for this test, I'd probably put 2-6-6 as my answer and maybe a parenthetical comment about it depending on what I thought of the test administrators. Some professors would be delighted to have this flaw pointed out (I think most of my philosophy and definitely all of my logic professors would), some would be annoyed and mark anything other than 2-6-6 as wrong. Honestly, this sounds like a pretty silly competition, maybe one step above awarding scholarships based on the answers to trivial pursuit questions, so maybe I'd err on the uncritical interpretation. But it's still a flawed question, the premises don't guarantee the truth of the conclusion, even though the boy in the puzzle thinks they do.
posted by skewed at 1:21 PM on March 23, 2011
I guess the correct answer is "there is not enough information to be certain the ages of the children, even though it seems like 2-6-6 is the intended answer." As it is, there are certain assumptions underlying the "correct" answer that are not unambiguously valid. Obviously, if I were to be sitting for this test, I'd probably put 2-6-6 as my answer and maybe a parenthetical comment about it depending on what I thought of the test administrators. Some professors would be delighted to have this flaw pointed out (I think most of my philosophy and definitely all of my logic professors would), some would be annoyed and mark anything other than 2-6-6 as wrong. Honestly, this sounds like a pretty silly competition, maybe one step above awarding scholarships based on the answers to trivial pursuit questions, so maybe I'd err on the uncritical interpretation. But it's still a flawed question, the premises don't guarantee the truth of the conclusion, even though the boy in the puzzle thinks they do.
posted by skewed at 1:21 PM on March 23, 2011
If the puzzle weren't filtered through these characters, I feel like you might be able to argue differently. But to me, there's no question in this case.
Great point! Can't believe we've all missed The Fourth Clue!
posted by muddgirl at 1:25 PM on March 23, 2011
Great point! Can't believe we've all missed The Fourth Clue!
He says: "Aha", and gives her the correct ages of her brothers.Quite a well-written question after all!
posted by muddgirl at 1:25 PM on March 23, 2011
Oooh, I've got the perfect place to reuse this! Thanks.
posted by doub1ejack at 5:23 PM on March 23, 2011
posted by doub1ejack at 5:23 PM on March 23, 2011
I object to all these quibbles about ages of twins and adopted siblings etc...
This is a MATH problem wrapped in words to make it interesting. They could have worded it simply as:
1) Find all the ways to factor 72 into three integers
2) Add all the factors from each choice and find any that add to the same number
3) Find which one has the largest common factors
Of course this way would be boring and fourmulic.
posted by Confess, Fletch at 8:56 AM on March 24, 2011
This is a MATH problem wrapped in words to make it interesting. They could have worded it simply as:
1) Find all the ways to factor 72 into three integers
2) Add all the factors from each choice and find any that add to the same number
3) Find which one has the largest common factors
Of course this way would be boring and fourmulic.
posted by Confess, Fletch at 8:56 AM on March 24, 2011
This is a MATH problem wrapped in words to make it interesting.
This is why we don't allow English majors in the Math department.
posted by banshee at 10:34 AM on March 24, 2011
This is why we don't allow English majors in the Math department.
posted by banshee at 10:34 AM on March 24, 2011
This thread is closed to new comments.
posted by jannw at 7:23 AM on March 23, 2011