Simple Maths Problem
Discussion
Einion Yrth said:
RATATTAK said:
7/24 for me but ... consider this:
If a brick weighs 7 lbs plus half a brick, how much does a brick and a half weigh ?
21 lbs - seems a bit heavy for a brick, but...If a brick weighs 7 lbs plus half a brick, how much does a brick and a half weigh ?
Alias218 said:
I hate to say it, and I'm more than a little embarrassed, but I think you may be correct.
Haha, well done for fessing up Alias.FWIW I have a Maths degree and my first thought was obviously it's 7/24. (If you've ever read "Thinking Fast and Slow" it explains why that happens).
But it ain't, as explained above it's 7/48.
Which begs the question who on earth set that terrible question AND gave the wrong answer.
Monty Hall problem anyone?
Greg66 said:
Alias218 said:
I hate to say it, and I'm more than a little embarrassed, but I think you may be correct.
S’ok.For a laugh once I said to a very clever guy I know with a science background: metals expands when you heat it, right? He agreed. I have a metal washer. I heat it. What happens to the hole in the middle?
So keen was he to press upon me how rapidly he could solve this that he blurted out: “it gets smaller!”
Pause
“No! It stays the same size!”
Then looked a bit anxious, he said “I need to go away and think about this” and literally ran from the room a la Sheldon Cooper.
He came back 20 mins later with the right answer confessing that he had rarely been so embarrassed.
I was very understanding. I pointed at him and laughed loudly for about ten minutes.
I think the only way to get over this sort of thing is to be laughed at! Builds humility.
Greg66 said:
Haha! Monty Hall is great and completely counter-intuitive. Sometimes even after the answer is explained...
Many years ago we had the Monty Hall debate in our office and one chap, senior and very well educated, just would not accept the answer. We had to create a mockup of the problem using flipcharts and go through the motions to see what results came out. Unfortunately out of about 20 goes we only won something like 11 times by switching so closer to his wrong answer than the correct one! So he still wasn't convinced.I don't think it matters how the question is worded:
'Cakes' If you think of the cakes individually, then there is 1/6 left of one and 1/8 left of the other. That's the answer if you want to talk about the cakes seperately. This is the same as 4/24 of one and 3/24 of the other.
'Cake' If you think of the 2 cakes together, the answer remains the same 4/24 and 3/24.
People are conflating the idea of 24 slices and 2 cakes to get 7/48. Just because you are working in 24ths doesn't mean that you need to work in 48ths because you have 2 cakes. If you work in 48ths and then say that the cakes have 3 and 4 slices left, then you have got the amount eaten wrong.
'Cakes' If you think of the cakes individually, then there is 1/6 left of one and 1/8 left of the other. That's the answer if you want to talk about the cakes seperately. This is the same as 4/24 of one and 3/24 of the other.
'Cake' If you think of the 2 cakes together, the answer remains the same 4/24 and 3/24.
People are conflating the idea of 24 slices and 2 cakes to get 7/48. Just because you are working in 24ths doesn't mean that you need to work in 48ths because you have 2 cakes. If you work in 48ths and then say that the cakes have 3 and 4 slices left, then you have got the amount eaten wrong.
Northbloke said:
Greg66 said:
Haha! Monty Hall is great and completely counter-intuitive. Sometimes even after the answer is explained...
Many years ago we had the Monty Hall debate in our office and one chap, senior and very well educated, just would not accept the answer. We had to create a mockup of the problem using flipcharts and go through the motions to see what results came out. Unfortunately out of about 20 goes we only won something like 11 times by switching so closer to his wrong answer than the correct one! So he still wasn't convinced.
Questions like the cake one are probably hell for anyone on the autistic spectrum.
boyse7en said:
OK, i'm a bit lost in all the too-ing and fro-ing with various explanations and kind of lost the thread of who was arguing for which answer.
Have we finally come to a consensus that the answer is "7/48 of the cakes are left"?
Not sure if it's a consensus, but that's the right answer.Have we finally come to a consensus that the answer is "7/48 of the cakes are left"?
dr_gn said:
Toltec said:
dr_gn said:
Not sure if it's a consensus, but that's the right answer.
The one in the answer section of the book, yes?Toltec said:
dr_gn said:
Toltec said:
dr_gn said:
Not sure if it's a consensus, but that's the right answer.
The one in the answer section of the book, yes?I can draw a diagram to explain it if you like, but it’s really not difficult to understand once you get beyond what you automatically tend to calculate vs. what they actually ask.
dr_gn said:
Worded incorrectly for the answer they gave, NOT ambiguously. Their answer was stated on page 1 of this thread BTW.
I can draw a diagram to explain it if you like, but it’s really not difficult to understand once you get beyond what you automatically tend to calculate vs. what they actually ask.
Just asked the question of two very smart people, 50/50 split on the answer, however the 7/48 was partially because he took it that the question must be non-trivial as I had asked it so chose the less obvious answer. Which is the point you are making clearly.I can draw a diagram to explain it if you like, but it’s really not difficult to understand once you get beyond what you automatically tend to calculate vs. what they actually ask.
Interestingly if you want to pick hairs the idea that two cakes could actually be identical was questioned, however we reached the hypothesis that the cakes had been produced from a master cake using a quantum level duplication device of some kind and the slices cut almost instantaneously thereafter.
I guess it comes down to assessing how likely it was the setter made a mistake or not, if you do not know the person or have not encountered previous tests set by this person, or at a lower utility similar tests by other people, then it becomes harder to assign a probability to this. I decided that the balance of probability was the question was poorly worded and therefore chose the answer that the setter obviously expected to receive.
Toltec said:
dr_gn said:
Worded incorrectly for the answer they gave, NOT ambiguously. Their answer was stated on page 1 of this thread BTW.
I can draw a diagram to explain it if you like, but it’s really not difficult to understand once you get beyond what you automatically tend to calculate vs. what they actually ask.
Just asked the question of two very smart people, 50/50 split on the answer, however the 7/48 was partially because he took it that the question must be non-trivial as I had asked it so chose the less obvious answer. Which is the point you are making clearly.I can draw a diagram to explain it if you like, but it’s really not difficult to understand once you get beyond what you automatically tend to calculate vs. what they actually ask.
Interestingly if you want to pick hairs the idea that two cakes could actually be identical was questioned, however we reached the hypothesis that the cakes had been produced from a master cake using a quantum level duplication device of some kind and the slices cut almost instantaneously thereafter.
I guess it comes down to assessing how likely it was the setter made a mistake or not, if you do not know the person or have not encountered previous tests set by this person, or at a lower utility similar tests by other people, then it becomes harder to assign a probability to this. I decided that the balance of probability was the question was poorly worded and therefore chose the answer that the setter obviously expected to receive.
It’s as much about wording as maths, but I really can’t see how anyone could assume the answer related to a single cake - the wording is not even ambiguous - it’s definitely plural, not singular.
The only way the answer could be 7/24 was if it explicitly said “...a cake...”
Or am I missing something more subtle in the wording or maths?
Imaginr if you had two cakes, a quarter of the first cake was eaten and three quarters of the second cake was eaten then:
Three quarters of the first cake would remain.
One quarter of the second cake would remain.
If you were to simply add 3/4 to 1/4 you'd get 4/4 =1/1=100% remaining. That's simply impossible and shows quite clearly you shouldn't just add the fractions without first considering whether the initial number of items was something other than 1.
Three quarters of the first cake would remain.
One quarter of the second cake would remain.
If you were to simply add 3/4 to 1/4 you'd get 4/4 =1/1=100% remaining. That's simply impossible and shows quite clearly you shouldn't just add the fractions without first considering whether the initial number of items was something other than 1.
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