A small problem to peruse.

Ambient Fish

Active Member
I would just open the boxes and look:thumbsup: :D
 

Steven

Senior Moderator
One from each box.

I've seen this one in apples and bananas form :D - in that version it's stipulated you can't peek at whole box. However the answer is post 2 if you deliberately left that detail out

edit: you didn't say you want an explanation
 

Drd

Well-known Member
Just 1 piece from the apples and orange case?
 

Jammyb

Well-known Member
He needs to check every peice in every box.

"A retailer has bought 3 boxes of fruit. He paid less as they are all wrongly labelled."

That is all we know for sure, the boxes may contain no apples and no oranges, they might be full of something else. Each box might contain an assortment.

Can I have a job now please?
 

Steve N

Distinguished Member
He just needs to open one box.
We know they all are labelled wrongly.
So by opening one he effectively has two pieces of information.
1, what is in that box.
2, what label was on that box.
Therefore:-
If the one he opens has the mixed apples & oranges in then he knows that the other two boxes are a box of apples and a box of oranges.
His mixed box will have been labelled wrong.
So if, for example, his opened box had been labelled oranges then the apple box would have the apples & oranges label and the oranges box would have the apple label.

The clue is in the fact that they are all labelled wrong.
 

imightbewrong

Distinguished Member
If he can only check one piece from each box he needs to take one from the box labelled Apples and Oranges. If he can open the lid and look in, he can look in any one box.

Here's a follow up question:

A man takes two fruit from one box at random. If he takes them from the mixed box he takes one of each fruit, otherwise he takes two the same. He shows you one of the fruit he has taken and it is an apple. What is the probablitlty the other is also an apple?

Enjoy.
 

Uridium

Well-known Member
sean5302 said:
I see, on another post, that the GCSE results are out, today.

In my company, we employ hundreds of graduates, from all over Europe. Some have excellent qualifications, but struggle with basic problem-solving, so I have one or two tests of my own.
I see this almost every day with Graduates, a fistfull of qualifications but less common sense than my 8yr old son!

IT contractors seem to be the worst, leave university with a degree in something irrelevant, go to an MSCE boot camp for more irrelevant qualifications and then get a support job through an agency. Show them a problem that isn't "Textbook" ,involves some analytical thinking and common sense and they're stumped.

Fortunately the company i work for "black marks" rubbish contractors so we only see them the once. Still a pain in the butt training the next one that comes along though.
 

Steven

Senior Moderator
I'm about to start uni

PM me in 3 years :rotfl:
 

SeanT

Well-known Member
But they could still be a box of grapes, a box of nectarines, and a box of apples, if he only opens one box???
 

Mr_Wistles

Distinguished Member
uridium said:
I see this almost every day with Graduates, a fistfull of qualifications but less common sense than my 8yr old son!
Show a graduate how to do something and they will copy it perfectly.

Ask them to think on their own 2 feet, error, error.
 

mickrick

Banned
sean5302 said:
Yes, if we check the box marked "apples and oranges" it could contain just apples, or just oranges, as it's wrongly labelled.

If we pull an orange out we know it's really oranges.
If that contains the oranges, the box labelled "oranges" must contain apples and the box labelled "apples" must contain apples and oranges.
But if you open a box marked "apples and oranges" and blindly pick one item of the contents, you have a 50% chance (providing there are equal numbers of both fruit of course) of pulling out an apple or an orange. So you would have to either keep pulling out fruit until you either a) have pulled out all oranges or b) pull out an apple. Then you can determine the contents. Or else open the case and inspect the contents in whole. So your answer is incorrect.
 

imightbewrong

Distinguished Member
mickrick said:
But if you open a box marked "apples and oranges" and blindly pick one item of the contents, you have a 50% chance (providing there are equal numbers of both fruit of course) of pulling out an apple or an orange. So you would have to either keep pulling out fruit until you either a) have pulled out all oranges or b) pull out an apple. Then you can determine the contents. Or else open the case and inspect the contents in whole. So your answer is incorrect.
We only need to pull out one from the O&A box because we know that it definately does not contain both - because all boxes are wrongly labelled. SO if we pull out an apple we know this is the apple box, the one labelled apples contains oranges (because the one labelled oranges cannot) and the one labelled oranges has both types.
 

mickrick

Banned
imightbewrong said:
We only need to pull out one from the O&A box because we know that it definately does not contain both - because all boxes are wrongly labelled. SO if we pull out an apple we know this is the apple box, the one labelled apples contains oranges (because the one labelled oranges cannot) and the one labelled oranges has both types.
Of course. I'll get me coat.:oops:
 

krish

Distinguished Member
Thanks Sean :smashin:
I love these logic problems
- great way to clear away the cranial cobwebs ;)
 

imightbewrong

Distinguished Member
imightbewrong said:
Here's a follow up question:

A man takes two fruit from one box at random. If he takes them from the mixed box he takes one of each fruit, otherwise he takes two the same. He shows you one of the fruit he has taken and it is an apple. What is the probablitlty the other is also an apple?
No takers? :D
 

colinwheeler

Active Member
Not enough information provided. Is the fruit bought the same as the labels, just mis-labeled in each box? I.e. no pears or peaches. If you then know that each box is labled incorrectly, then you can deduce contents, not having to check all the boxes.

However Schrodinger would say that, they are not oranges, apples or oranges and apples until you have opened up the boxes to observe them due to chaos theories. So they could be grapes, or kittens, you never know.
 

Steven

Senior Moderator
Surely you'd be able to hear kittens? If not...smell them?

Either way the RSPCA are a-coming
 

colinwheeler

Active Member
No, the plutonium with the kittens keeps them quiet and squeeky clean...did you not know that about plutonium?

Edit: Cross thread I know...lol...but can we still call it plutonium or do we now have to call it astoroidium or can'tdefinium.
 

Jammyb

Well-known Member
The original question should say:

You have a box of oranges, a box of apples and a box of apples and oranges. However the labels have been mixed up so that they are all incorrect.

Or something to that effect.

Because as the question stands my answer is correct and everyone else is trying to overthink the question in a "where did they bury the survivors?" style
 

imightbewrong

Distinguished Member
Drd said:
That's the obvious answer, but it's incorrect.

Anyone else?
 

imightbewrong

Distinguished Member
Jenn said:
Any non 50% guesses should be accompanied by a bit of reasoning please :)
 

Jenn

Well-known Member
imightbewrong said:
Any non 50% guesses should be accompanied by a bit of reasoning please :)
Well if he picks an apple first it means he's picked from either the all apple basket or the apple and orange basket.
If he picked the apple from the all apple basket, there's 100% (or 1 out of 1) chance that the second pick is an apple.
If he picked the apple from the apple and orange basket there's 50% (or 1 out of 2) chance that the second pick is an apple.

So in total there's 2 chances out of 3 that the second pick will be an apple (or 66%).
 

imightbewrong

Distinguished Member
Jenn said:
Well if he picks an apple first it means he's picked from either the all apple basket or the apple and orange basket.
If he picked the apple from the all apple basket, there's 100% (or 1 out of 1) chance that the second pick is an apple.
If he picked the apple from the apple and orange basket there's 50% (or 1 out of 2) chance that the second pick is an apple.

So in total there's 2 chances out of 3 that the second pick will be an apple (or 66%).
Bravo. Basically when he shows you an apple one of three equally likely things has happened

- He went to the Apples basket and is showing you his left hand
- He went to the Apples basket and is showing you his right hand
- He went to the Apples & Oranges basket

The first two lead to an apple in his other hand, hence a 2/3s chance of second apple.

I like to ask this one to inteview candidates and watch their face make funny shapes while they figure it out.
 

Jenn

Well-known Member
imightbewrong said:
Bravo. Basically when he shows you an apple one of three equally likely things has happened

- He went to the Apples basket and is showing you his left hand
- He went to the Apples basket and is showing you his right hand
- He went to the Apples & Oranges basket

The first two lead to an apple in his other hand, hence a 2/3s chance of second apple.

I like to ask this one to inteview candidates and watch their face make funny shapes while they figure it out.
I had to put it to paper to be honest. :)
And I wasn't that good at statistics at school but I obviously picked up the basics.

To be honest I don't think these tests give an accurate indication on a person's ability to do their job (unless they're applying to work with statistics !). I can't remember the last time I had to use statistics in my job.
And as for the first test posted here, in real terms you'd open all the baskets, swear a bit then phone your supplier and have a go at them ;) ; not spend time working out the result by taking a fruit here and there.
 

WibXL

Well-known Member
Any chance of some more?
 

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