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Ultimate math trick question?

The Pro from Dover said:
I'm curious. What was the answer given by the source of the question? And, can you provide a link?
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I googled the phrasing. There were many variations on the problem, most from Algebra I teachers. The answer they gave was 14, or whatever their particular variation on the problem required.


(I,e, in some cases, the brother was six years old, and the final age was 100, but it was all the same idea.)
 
Red Baron Farms said:
She could be born February 29th and you born on March 1st two years earlier. when you reach 4, she would be 1/2 your age but with a birthday prior to yours in February instead of March. Since leap day babies celebrate their birthdays on February 28th in non-leap years, 10 years later for 1 day you might be 13 while she was 12. It’s cheating a bit, certainly pedantic, but it could be conceived as such. This is different than understanding 4 years means 4 years + up to 364 days in common usage of the term, and half means exactly that, half.
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Why? Just because you say so? Seems arbitrary and neither consistent or logical. Why would you cite common usage for part of the problem and then ignore it for another part? If someone says "Mick Jagger married a woman half his age" do you think they figured out the exact moments of both of their births? Based on common usage what do you think the answer to this questions is? - When I was 4 years old, my sister was half my age. When I was 4 years old how old was my sister?
 
The math puzzle (and its variants) is strictly designed to trap people who might think that if she was once "half the age" then she will always be half the age. That's all it's about and the correct answer is 14.

It doesn't work the way RBF wants it to work because of the way the question is worded. He would have gotten many "complete correct answers" if it had been worded differently, like this...

Instead of How old am I?, it should have been worded How old might I be?. This informs us that the questioner is willing to accept multi-answers and may actually be seeking the multi-answer.

It's really a messed up quiz and that isn't sour grapes. It's a turd because one of the "necessary" numbers is guaranteed to be incorrect. The person is either 14 or 15 and so you have to include the wrong age in order to provide the desired answer. That's not a trick question to discover intelligence or mathematical ability. It's also why 1700+ people did not get it "right".

When you see an online quiz like this where nobody out of 1700+ gets the "ultimate complete answer", you shouldn't right away think that there are no smartees in that bunch. You should think that you are not thinking straight.
 
William Parcher said:
The math puzzle (and its variants) is strictly designed to trap people who might think that if she was once "half the age" then she will always be half the age. That's all it's about and the correct answer is 14.

It doesn't work the way RBF wants it to work because of the way the question is worded. He would have gotten many "complete correct answers" if it had been worded differently, like this...

Instead of How old am I?, it should have been worded How old might I be?. This informs us that the questioner is willing to accept multi-answers and may actually be seeking the multi-answer.

It's really a messed up quiz and that isn't sour grapes. It's a turd because one of the "necessary" numbers is guaranteed to be incorrect. The person is either 14 or 15 and so you have to include the wrong age in order to provide the desired answer. That's not a trick question to discover intelligence or mathematical ability. It's also why 1700+ people did not get it "right".

When you see an online quiz like this where nobody out of 1700+ gets the "ultimate complete answer", you shouldn't right away think that there are no smartees in that bunch. You should think that you are not thinking straight.
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+1
 
Red Baron Farms said:
I get that, which is why I have always agreed that 14 is correct, just incomplete.

It bears understanding that the problem did NOT say she was 2 though.
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Stating the problem in this way does not remove any ambiguity as you seem to assume. The primary source of ambiguity in the problem comes from "half my age". On one end of the scale, you have just the common interpretation where someone is half your integer age. On the other end, you have half your age down to the millisecond. The other smaller source of ambiguity is whether leap years, leap seconds, and time zones are considered.

Counting for timezones and leap years, there are cases where you just turned 4 and your sister is half your age down to the millisecond and is still 1.

Claiming to have the only right answer on this is either hubris or ignorance, I'm not sure which.
 
Red Baron Farms said:
a person who is "4" is actually between "4" and "4 years+364 days" due to always rounding down.

So the sister will be between "2" and "2 years 182 days" younger, being half your age.
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Incorrect even by your own logic. Due to "always rounding down", the maximum difference between them (assuming we are not going to smaller units than days) is between exactly 2 years old and 4 years 364 days.

That's a difference of 2 years 364 days. Not 2 years 182 days.
 
phunk said:
Incorrect even by your own logic. Due to "always rounding down", the maximum difference between them (assuming we are not going to smaller units than days) is between exactly 2 years old and 4 years 364 days.

That's a difference of 2 years 364 days. Not 2 years 182 days.
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His claim is that the problem should be considered by calculating your age in days, and then halving that number of days to get your sister's age and any other interpretation is wrong.
 
William Parcher said:
It's really a messed up quiz and that isn't sour grapes. It's a turd because one of the "necessary" numbers is guaranteed to be incorrect. The person is either 14 or 15 and so you have to include the wrong age in order to provide the desired answer. That's not a trick question to discover intelligence or mathematical ability. It's also why 1700+ people did not get it "right".

When you see an online quiz like this where nobody out of 1700+ gets the "ultimate complete answer", you shouldn't right away think that there are no smartees in that bunch. You should think that you are not thinking straight.
Click to expand...


The “right” answer would involve solving it as written. While it may not always be what people mean when they say “I’m x years old” if they don’t give some measure of precision, the correct thing to do is assume they are exactly that old. 14 is therefor the right answer but it doesn’t hurt to be aware than the person asking the question probably wasn’t being precise enough for you to know for sure if that is what they really meant. Anyway, there is no real trick here, just an insufficiently precise question.

Not a great trick question but here is one I liked when I was 12 (and my sister was 14)

Three men are driving cross country when their car breaks down and can’t be fixed until the next day. They stay in a hotel which charges $250 for the night, but bank machine isn’t working they only have $100 bills, so they get the desk clerk to give them their change in the form of 5 * $10 bills. They each take 1, and leave the desk clerk 2 as a tip. The room therefor cost each of them 3 * $90, plus $20 for the tip, which comes to $290. What happened to the other $10?
 
Red Baron Farms said:
I see what you are saying as to why it annoys you, however it is your inconsistency that makes it annoying.

For example, "When a child says "I'm four years and three months old," the statement is almost always belittled. " You are exactly correct here. 4 years 3 months is commonly referred to as 4.

But then you state that, " If she turned two after I turned four, there will be a period during which I was four and she was one, as well as a period during which I was four and she was two, and during some of her age, I will be three years older, not two." This is the part that does not follow. While the years convention is true, your age in relation to hers never really varies. You are always the same number of years older than her.(and days) That always remains fixed. So you have tricked yourself.
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I disagree. Of course in one sense one is always the same amount younger or older, but not in the common way language is used. If you are four and she is two, you can be said to be nominally two years older, whether that condition lasts a day or a year.
 
lomiller said:
Three men are driving cross country when their car breaks down and can’t be fixed until the next day. They stay in a hotel which charges $250 for the night, but bank machine isn’t working they only have $100 bills, so they get the desk clerk to give them their change in the form of 5 * $10 bills. They each take 1, and leave the desk clerk 2 as a tip. The room therefor cost each of them 3 * $90, plus $20 for the tip, which comes to $290. What happened to the other $10?
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The tip was part of the 3*90, not in addition to it. 3*90 = 250+20 = 300-(3*10)
 
lomiller said:
The “right” answer would involve solving it as written. While it may not always be what people mean when they say “I’m x years old” if they don’t give some measure of precision, the correct thing to do is assume they are exactly that old. 14 is therefor the right answer but it doesn’t hurt to be aware than the person asking the question probably wasn’t being precise enough for you to know for sure if that is what they really meant. Anyway, there is no real trick here, just an insufficiently precise question.

Not a great trick question but here is one I liked when I was 12 (and my sister was 14)

Three men are driving cross country when their car breaks down and can’t be fixed until the next day. They stay in a hotel which charges $250 for the night, but bank machine isn’t working they only have $100 bills, so they get the desk clerk to give them their change in the form of 5 * $10 bills. They each take 1, and leave the desk clerk 2 as a tip. The room therefor cost each of them 3 * $90, plus $20 for the tip, which comes to $290. What happened to the other $10?
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The room only cost them 3*90, including the tip. So there isn't a missing ten. The other $30 is their change.
 
I was hoping* to see an actually interesting math question, like the derivative of xx. Instead, it's just stupid stuff which relies on a particular and not obvious interpretation of the phrasing of the question, rather than the actual math.

* Note that I said hoping, not expecting. I'm not that naive.
 
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