Was bored today and searched for a puzzle. Came across this one....

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In summary, the problem is asking for the number of gifts wrapped per hour in the last 45 hours when working with a colleague, given that in the first 15 hours, one person wrapped 4 gifts per hour and in the next 45 hours, the combined rate of two people wrapping was 7 gifts per hour. The first part about the one person working alone is not needed to solve the problem, but it provides context for the situation. Ultimately, the solution is found by finding the combined wrapping rate and then subtracting the rate of the one person working alone.
  • #36
DaveC426913 said:
Because, again, the answer works out to 8 exactly, no rounding, no fractions. It would be a fabulous coincidence if that happened by accident due to a misinterpretation. The riddle author has chosen the numbers carefully to arrive at the answer without any math more complicated than 3-digit arithmetic.
It appears that you are stating this, correctly I believe, to deaf ears. For reasons I don't understand, some people just don't seem to want to believe it.
 
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  • #37
phinds said:
It appears that you are stating this, correctly I believe, to deaf ears. For reasons I don't understand, some people just don't seem to want to believe it.
In their defense, it's not a black and white issue. In our opinions "it's dark grey enough that I think it was meant to be black".
1653923226548.png

And others are of the opinion that "Dark grey is just a mix of black and white, and opinions are cheap." which is not, technically, wrong. :wink:
 
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  • #38
True. I DO understand the logic behind their point of view but I firmly believe that you have it right. As I posted in post #2 I consider the problem to be trivial. I immediately rejected the, in my view, incorrect interpretation and solved the problem in my head almost immediately, so it did not occur to me to take the alternate interpretation seriously and I still can't take it seriously.

Part of the reason for all that is that, as you have pointed out, the math is trivial using the, to me, obvious interpretation.
 
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  • #39
Borg said:
The meaning of a sentence like that one shouldn't change if you reverse it. If you have to modify the reversal in order for it to make sense, then the original sentence wasn't clear. When your modified phrase is reversed, it makes more sense as to its intent.

because a colleague helped for the next 45 hours, the amount of gifts wrapped rose to seven per hour
My reversal was keeping the sentence the same, yours wasn't. The ability to change a sentence by changing it isn't telling us anything.
 
  • #40
mfb said:
My reversal was keeping the sentence the same, yours wasn't. The ability to change a sentence by changing it isn't telling us anything.
OK, let's try it another way.
In a department store, with only one girl working on the gift-wrapping service, four gifts per hour were wrapped in the first 15 hours. With help from a colleague for the next 45 hours, the amount of gifts wrapped rose to seven per hour. How many gifts were wrapped each hour in the last 45 hours only?
I still find the problem to be highly misleading given the stated answer. As I read through the paragraph, the first sentence states a gift wrapping rate that is an hourly rate and also happens to be the total average hourly rate. The second sentence refers to a time period of 45 hours and a rate of seven per hour. However, it does not specify whether that rate was an hourly rate for the 45 hour period or was a total average hourly rate for the entire (or per @phinds an OVERALL) 60 hour period. With the way that it's written, "the next 45 hours", can easily be construed as being the object of the stated seven per hour rate and would therefore be an average for that time period.

To me, this looks like a trick question that's asking for an answer that they give in the second sentence. If I change the question being asked in the third sentence, the meaning of the information given in the first two sentences should not change (I hope everyone agrees on that at least). How would everyone solve this question given no change in the first two sentences?
What was the average number of gifts wrapped per hour for the entire 60 hours?
Would people assume that this one was the trick question because the 7/hour rate given in the second sentence was an overall rate as many are stating about the original question? Or would the assumption now be that the reader should perform a different calculation because the question is different?
 
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  • #41
I totally did not expect to contribute to this thread, but here we go.

Long story short, the ambiguity is whether we interpret the given rates ("four gifts per hour were wrapped in the first 15 hours," and "the amount of gifts wrapped rose to seven per hour") as instantaneous rates, or average rates. Do we have enough information to tell? I think we do. Let's break it down.

Assumptions:
We should assume that the actual instantaneous rates (given or not) are uniform. Sure it could happen that the girl or girls slowly and gradually improved their gift wrapping skills over the course of the 60 hours. But let's rule that out; there's not enough information in the puzzle statement to justify continuously variable, instantaneous rates. Instead, let's assume that for the first 15 hours, there is a constant, uniform instantaneous rate, and for the next 45 hours there is a separate, but constant, uniform, instantaneous rate.

So the real question is, does the "seven per hour" figure in the "for the next 45 hours, the amount of gifts wrapped rose to seven per hour" statement refer to the instantaneous rate or average rate?

Instantaneous hypothesis:
If we assume that the "seven per hour" figure refers to the instantaneous rate, then the puzzle makes no sense as a puzzle at all. The crux of the riddle -- its final question -- is clearly asking for the instantaneous rate during the last 45 hours only. So if the "seven per hour" refers to that, it's not much of a riddle at all. It just gave you the answer in the preceding sentence.

Average hypothesis:
The key wording leading to this hypothesis is "rose to." The verb is ambiguous in that the change can happen instantaneously, but there is a connotation in "rose to" that the change happens gradually; that's the connotation. Accordingly, this leads to reader to surmise that the "seven per hour" figure is the average rate, and true (i.e., true to be "seven per hour") only after considering the entire 60 hour timeframe.

Conclusion:
So (in my opinion) there is enough information in the riddle to conclude that @DaveC426913's analysis in post #29 is correct. Although there is some ambiguity in the riddle, I believe the puzzle's wording sufficiently addresses the ambiguity such that there is only one, clear interpretation. Thus the clear answer is 8 gifts per hour.
 
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  • #42
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  • #43
It was an informative discussion and they all clearly agreed that the wording was a mess. However, I am now changing my opinion of what the wording meant.

One post pointed out this pair of options for the placement of the comma in the second sentence:

With help from a colleague for the next 45 hours, the amount of gifts wrapped rose to seven per hour.
With help from a colleague, for the next 45 hours the amount of gifts wrapped rose to seven per hour.


The original question is written like the first sentence which places the emphasis for the rate away from the colleague's help. It's still a linguistic mess but if I had to pick two meanings for the rates in those two sentences, it's pretty clear which one goes with each sentence.
 
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  • #44
Dunno, I'm kinda partial to this:
Jarvis323 said:
2) Author intended it to be ambiguous and the real problem is meant to be about understanding/guessing intended meaning from inaccurate and imprecise language based on context.
Remember, this was an online riddle - not necessarily strictly a math problem.
 
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  • #45
I mentally translated it to this:

"I stopped to fill up with gas, and reset my trip odometer and mileage. At 15 miles the average mileage showed 4 miles per gallon. At 60 miles, the average read 7 miles per gallon. What was my average mileage for the last 45 miles?"

But I have recently been on a long driving trip and have been thinking of such calculations. Plus (confirmation bias?) this works out to the given answer, 8 (as mentioned several times, above).
 
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  • #46
gmax137 said:
I mentally translated it to this:

"I stopped to fill up with gas, and reset my trip odometer and mileage. At 15 miles the average mileage showed 4 miles per gallon. At 60 miles, the average read 7 miles per gallon. What was my average mileage for the last 45 miles?"

But I have recently been on a long driving trip and have been thinking of such calculations. Plus (confirmation bias?) this works out to the given answer, 8 (as mentioned several times, above).
This is further less clear than the originally given giftwrappers girl & colleague example.
 
  • #47
symbolipoint said:
This is further less clear than the originally given giftwrappers girl & colleague example.
Maybe because I do a lot of driving, and I am used to grappling with the concept of a running average of gas mileage.

But the way gmax phased it removes the ambiguity in the original problem:

- reset my trip odometer
- At 15 miles the average mileage showed 4 miles per gallon
- At 60 miles, the average read 7 miles per gallon.


Since the reset was explicitly mentioned at the start, we can logically conclude that it was not reset anywhere else - (such as: at the 15 mile mark).

Which means the average of 7mpg must needs apply to the entire 60 miles.
 
  • #48
Hmmm...appears to have turned out that the question actually wasn't trivial at over 40 replies later. This is because of the question's poor wording. It is a trivial question if it is worded correctly. Thanks for the solution that was posted which cleared up the confusion for me. And no it wasn't a homework problem.
 
  • #49
@haynewp
Where did the original question come from or where did you find it?
 
  • #52
haynewp said:
"...rose to..."
Now this would be along the lines of NOT instantaneous change, but been a gradual change. More credit for some who argued against our purely constant rates all-at-once interpretation.
 
  • #53
symbolipoint said:
"...rose to..."
The text is the same as in the OP. 🤔
 
  • #54
DaveC426913 said:
The text is the same as in the OP. 🤔
Yes, and only now after all the discussion & explanation here that "rose to" is carrying its meaning so that even I might understand the problem description a little better.
 
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  • #55
haynewp said:
So I am missing something in this one. The answr is 8. Can someone explain?
In a department store, with only one girl working on the gift-wrapping service, four gifts per hour were wrapped in the first 15 hours. With help from a colleague for the next 45 hours, the amount of gifts wrapped rose to seven per hour. How many gifts were wrapped each hour in the last 45 hours only?
The answer seems to be 7. It says that for time 15 < T < 60, the rate of gift-wrapping was 7, and if the final time is assumed to be 60 hours, then the last 45 hours was completely within that rate of 7 per hour. The rate for T < 15 is thus completely irrelevant.
 
  • #56
swampwiz said:
It says that for time 15 < T < 60, the rate of gift-wrapping was 7
No it doesn't.

Reread the OP, and then follow the thread, which has addressed the same mistake you've made.
 
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  • #57
DaveC426913 said:
No it doesn't.

Reread the OP, and then follow the thread, which has addressed the same mistake you've made.
Uh, yes it does, at least for the original wording.
 
  • #58
swampwiz said:
Uh, yes it does, at least for the original wording.
It is a somewhat natural reading, yes. But it is a reading that makes the subsequent question pointless. So it is a reading that would normally be ignored in favor of the somewhat more strained reading that results in a mildly interesting calculation.

It has been persuasively argued that the resulting ambiguity in the question is intentional. Which would make any disagreement about the true and correct reading pointless. There is no true and correct reading of an intentionally ambiguous statement.
 
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  • #59
jbriggs444 said:
It is a somewhat natural reading, yes. But it is a reading that makes the subsequent question pointless. So it is a reading that would normally be ignored in favor of the somewhat more strained reading that results in a mildly interesting calculation.

It has been persuasively argued that the resulting ambiguity in the question is intentional. Which would make any disagreement about the true and correct reading pointless. There is no true and correct reading of an intentionally ambiguous statement.
I agree that the original wording makes it pointless question, other than to be a trick question. The thing is, what part of the question shall be presumed mistaken? I didn't a single logical conclusion.
 
  • #60
Is this horse dead yet?
 
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  • #61
Yes. Please let it be dead.
 
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  • #62
swampwiz said:
Uh, yes it does, at least for the original wording.
It says "rises to 7".
 
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  • #63
DaveC426913 said:
It says "rises to 7".
LET IT BE DEAD !
 
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  • #64
Coming soon to theatres near you:

A girl falls in love with her race horse which dies, and she spends the rest of the movie studying spellcraft to bring it back to win the final race.

Necroprancer!
(You can't beat this dead horse!)
 
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  • #65
I think everything relevant has been said, repeating the same arguments yet another time wouldn't help.
 
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