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Ultimate math trick question?

I considered letting this slide, but I won't.

The reason that nobody gets "your" answer is that, although it is internally consistent, it is inconsistent with normal usage, and is therefor rejected without much thought.

You are 20 years, 180 days old. Your sister is 10 years, 91 days old.

Is your sister half your age?

By your standards, no. By everybody else's, yes. 10 divided by 20 is one half. And since you quite happily insisted on NOT explaining your peculiar standards as part of the question, you then get to play gotcha with the rest of the world. Trust me, nobody is impressed.

So go ahead and wonder why nobody takes the last step, but do not have the gall to claim that your usage is "right", and everybody else is wrong.
 
Kill the sister - her half existence is nonsense unless she is around 14. Or, let her live (2 yeas apart) with a twat of a brother until he dies.

Whichever, out of one of the 2, one must die to end this thread :)
 
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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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That was a favorite of mine too. But I am obviously much older than you, when I heard it the hotel room was only $25, and the question was "what happened to the extra dollar?"
 
Red Baron Farms said:
I get that, which is why I have always agreed that 14 is correct, just incomplete.
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Then you're wrong. You are relying on certain unstated assumptions while blithely ignoring certain other ones - children's ages are usually rounded up about a month before their birthdays in the West; neither person got in a rocket and flew around at .9c for a while.

There is no logical reason to accept your unstated assumptions or to reject others.

Your answer is illogical, you are wrong, and your reasoning is deeply stupid.
 
The OP first uses "years" in the colloquial sense, i.e., rounded down to a whole integer, but then when it comes to the phrase "half her age", suddenly expects microsecond precision. That's just plain disingenuous.

Ziggurat said:
I was hoping* to see an actually interesting math question, like the derivative of xx.
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Interesting? That's plain high school stuff.

x ^ x
= { definition of natural log }
(e ^ ln(x)) ^ x
= { exponentiation }
e ^ (x * ln(x))

and thus we get for its derivative:

d/dx (x ^ x)
= { see above }
d/dx (e ^ (x * ln(x)))
= { define y = x * ln(x) }
d/dx(e ^ y)
= { chain rule }
dy/dx * e ^ y
= { substitute back y }
d/dx(x * ln(x)) * e ^ (x * ln(x))
= { product rule }
( dx/dx * ln(x) + x * d/dx(ln(x)) ) * e ^ (x * ln(x))
= { derivative of ln }
( ln(x) + 1 ) * e ^ (x * ln(x))

For the proof format, see the work of E.W. Dijkstra and N. van Gasteren.

Oh, and can we please get LaTeX back?
 
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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matters little
Still only gives you 14 and 15 rather than 13 14 and 15.
WhatRoughBeast said:
I considered letting this slide, but I won't.

The reason that nobody gets "your" answer is that, although it is internally consistent, it is inconsistent with normal usage, and is therefor rejected without much thought.

You are 20 years, 180 days old. Your sister is 10 years, 91 days old.

Is your sister half your age?

By your standards, no. By everybody else's, yes. 10 divided by 20 is one half. And since you quite happily insisted on NOT explaining your peculiar standards as part of the question, you then get to play gotcha with the rest of the world. Trust me, nobody is impressed.

So go ahead and wonder why nobody takes the last step, but do not have the gall to claim that your usage is "right", and everybody else is wrong.
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SEE ABOVE. Same principle different numbers. net result is applied to the op would still give 14 and 15 as possibilities and not 13.
bruto said:
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.
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Reasonable. The question didn't say that, but if it did, your argument would be irrefutable.

The way the question is worded, without invoking some ridiculous scenario, the sister is always at minimum 2 years younger or more. This means rather than like what Mike answered:
Mike! said:
At least 13, but no more than 14.
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it goes the other way and is 14-15 not 13-14.

If the question said she was nominally 2 it would allow a 13 result. It said half. You can never 1/2 a number equal to or greater than 4 and get a number less than 2. So without the stupid pedantic results I promised NOT to bring to the puzzle, the answer can never include 13.

That's why I agree if we just want you say years only, 14 is an acceptable answer. But if we try to break it down to include more results like 15, then we can include 15 but not 13 without being willfully stupid about it. (like invoking leap years or time dilation/zones etc.)
 
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Red Baron Farms said:
The way the question is worded, without invoking some ridiculous scenario, the sister is always at minimum 2 years younger or more.

If the question said she was nominally 2 it would allow a 13 result. It said half. You can never 1/2 a number equal to or greater than 4 and get a number less than 2. So without the stupid pedantic results I promised NOT to bring to the puzzle, the answer can never include 13.
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And again, no. Please deal with my objection, rather than blowing it off. Let's take it by the numbers. Any discussion of my mistake must address the specific numbered statement.

1) I was 4 years, 1 months old. My sister was (at that time) 2 years, 7 months old.

2) Therefor, she was 2 and I was 4

3) and she was half my age, since 2/4 is one half.

4) When she is 13 years, 1 months old, I am 14 years, 7 months old.

5) At this time she is 13 and I am 14.

It is true that you have not resorted to "the stupid pedantic results I promised NOT to bring to the puzzle", you have substituted a different pedantic trick. You have expressed all ages in integral years, but insisted on computations which perform a round-down which is not explicitly identified and which flies in the face of conventional rounding when used with integral ages. A person who is 14 years, 8 months old is referred to as 14, not 15. And age ratios which do not specify other than integral ages do not support your calculation.
 
ddt said:
Interesting? That's plain high school stuff.
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Only if you figure out the appropriate substitution. Which a lot of people, even well past highschool calc, won't do. Without that, a lot of people struggle trying to figure out of they should treat it like a polynomial or an exponential, or if there's a way to apply chain rule directly. So while the solution can all be done with highschool level math, it's still quite tricky for most students at that level. Which is why I like the problem.

Oh, and can we please get LaTeX back?
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Yes, I miss that too. :(
 
I was 38 years when I visited this thread. After 5 pages, how big of a wanker is the OP?
 
Red Baron Farms said:
matters little
Still only gives you 14 and 15 rather than 13 14 and 15.
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Nope, you're wrong.

You see, not everyone considers babies 0 years old upon birth. Sometimes a baby right after birth is considered one year old. Thus, a four year old may have been born just three years ago. And someone exactly half their age would thus be born a year and a half ago. There will then be a period of time (6 months) when the older person is 13 while the younger person is 12.

Since you never specified which standard for reckoning ages your problem used, we must consider both possibilities, and 13 becomes a possibility again. So you were wrong.

And that's what you get for poorly constructing your problem in an attempt to confuse people.
 
When I was 4 years old, my sister was half my age.
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Wait, are you saying that for the entire time that you were 4, which is 364 days, your sister was half your age? It sure does seem like you are saying that. Do you guys have the same birthday with her being born 2 years after you? I kinda am curious because of what you said. Hey, where are you? You left the room and I have questions because of what you said. You asked me how old you are and I want to answer with some accuracy. Oh crap, you really are gone.
 
Ziggurat said:
Only if you figure out the appropriate substitution. Which a lot of people, even well past highschool calc, won't do. Without that, a lot of people struggle trying to figure out of they should treat it like a polynomial or an exponential, or if there's a way to apply chain rule directly. So while the solution can all be done with highschool level math, it's still quite tricky for most students at that level. Which is why I like the problem.
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Point taken. I retract the "plain" part of my statement.
 
William Parcher said:
Wait, are you saying that for the entire time that you were 4, which is 364 days, your sister was half your age? It sure does seem like you are saying that.
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That's a very good point. So we must bring in that relativistic time dilatation to realize that. And assume that sister keeps travelling away at the same speed for all those years.
 
ddt said:
That's a very good point. So we must bring in that relativistic time dilatation to realize that. And assume that sister keeps travelling away at the same speed for all those years.
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COME ON. Dont lose focus. It is a silly argument. He is being willfully ignorant. You can easily spot when someone does this. It's trivially easy. The form of the fallacious argument goes something like this:

"Wait, are you saying that (insert something clearly NOT said)"? Then argue how silly that thing was that wasn't said would be if it indeed was said.

It is not only fallacious reasoning, the fact WP has repeatedly used this fallacious arguing style on this thread is evidence (to me at least) why he lacks the critical thinking skills and logic ability to solve the OP in the first place, or even understand the explanation which came later.

People can disagree and I am perfectly fine with those here that don't agree but made sound arguments why they don't agree. However, if someone is forced to use a strawman logic fallacy or other unsound reasoning to back up their case, then it only shows they can't really back up their case. They either lack the intellectual tools, or are too lazy to think it through.
 
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