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Old Feb 28, 2005, 08:36 PM   #1
Daveway
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Impossible Brain Teezer

My teacher put a brain teezer out a few days ago and my class thinks it is impossible to figure out.

>>There are 3 crates holding apples and oranges. 1 crate is holding apples. 1 crate is holding oranges. Another crate is holding apples and oranges. The labels for the crates have been put on the wrong crates. You are allowed to open one crate. Which crate do you open to figure out what the other crates have in them? You must only open 1.<<

I'm convinced this is impossible and my teacher is just making a joke out of it.
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Old Feb 28, 2005, 08:49 PM   #2
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So you have three crates:

1) marked apples - contains ??
2) marked oranges - contains ??
3) marked A&O - contains ??

You open the one marked A&O. It has to be wrong, so it contains either apples or oranges. Suppose it contains apples:

1) marked oranges - cannot be oranges, cannot be apples, so it must be A&O
2) marked apples - cannot be apples, cannot be A&O (because the one marked oranges is), must be oranges.
3) marked A&O - contains apples

Suppose it contains oranges:

1) marked apples - cannot be apples, cannot be oranges (cuz the one you opened is), so it must be A&O.
2) marked oranges - cannot be oranges, cannot be A&O, so it must be apples.
3) marked A&O - oranges.

Doesn't this work?
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Old Feb 28, 2005, 08:54 PM   #3
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Hmmm, now that I think about it, can't you open any of the three crates and follow the same logic? If you open the oranges crate, which must contain apples or apples & oranges (since the label is wrong), then you can open the crate labelled with whatever is actually in the oranges crate, next, and it cannot contain its own label or the actual contents of the oranges crate, leaving only one option. Etc. So I'm not sure. It seems to me like you can open any of the three crates you want, and you'll get the answer.
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Old Feb 28, 2005, 08:55 PM   #4
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This is identical to the question about the 3 light bulbs.

3 light bulbs are located in a room without windows. there are 3 unmarked switches outside the room which supposedly switches on the light bulbs. You are allowed to walk out the room and go back in once and only once and you should be able figure out which switch is linked to which light bulb.

This is relatively easy once you figure it out

EDIT: you cannot see the light bulbs once you are out of the room or even the light from the bulbs

BTW, don't reveal the answer. let other people have the fun of answering
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Old Feb 28, 2005, 08:55 PM   #5
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Quote:
Originally Posted by daveway00
My teacher put a brain teezer out a few days ago and my class thinks it is impossible to figure out.

>>There are 3 crates holding apples and oranges. 1 crate is holding apples. 1 crate is holding oranges. Another crate is holding apples and oranges. The labels for the crates have been put on the wrong crates. You are allowed to open one crate. Which crate do you open to figure out what the other crates have in them? You must only open 1.<<

I'm convinced this is impossible and my teacher is just making a joke out of it.
Are the labels guaranteed to be wrong? or could they be right? Might the apple crate label be on the apple crate while the oranges and apples/oranges crates are switched?

If they are guaranteed to be on the wrong crates it doesn't matter which one you open first.

Say you open crate 1 that is labeled apples/oranges. If they are guaranteed to be wrong you will find either apples or oranges.

Say crate 2 is labeled apples and crate 3 is labeled oranges. If you found oranges in crate 1. Crate 3 has to contain apples or crate 2 is labeled correctly. You can swap any of the labels and come up with the same logic.

If the crates aren't all labeled wrong then I don't know where to start.

Edit: Beat to the punch and as always more eloquently than I can put it.
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Last edited by atszyman; Feb 28, 2005 at 09:04 PM.
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Old Feb 28, 2005, 09:00 PM   #6
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If all 3 crates are marked wrong, then they can contain anything but what is marked on them.

Open the first crate and find out what is in it. You know it'll be the label from one of the other two crates.

So you know it'll be one of the "other" two labels.

When you open the crate you'll be taking off a label and grabbing one from another crate and placing it on the crate you open.

The label in your hand is what is in the unopened crate with the label.
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Old Feb 28, 2005, 09:07 PM   #7
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Since we are on the subject of brain teaser, here's another one. (not sure if you guys have heard this one)

A father who recently died left a will to his 4 sons. the oldest son should get half of his asset, the second son should get a quarter of his asset, the third should get an 1/8 of the asset and the last should get a tenth of the asset. Unfortunately, the father left 39 sheeps to his sons, and the sons brought forth their case to you. How would you solve this?


EDIT: For those who want to have a shot at this, do not scroll down as the answer is a few post away
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Last edited by angelneo; Feb 28, 2005 at 09:21 PM.
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Old Feb 28, 2005, 09:11 PM   #8
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Quote:
Originally Posted by angelneo
3 light bulbs are located in a room without windows. there are 3 unmarked switches outside the room which supposedly switches on the light bulbs. You are allowed to walk out the room and go back in once and only once and you should be able figure out which switch is linked to which light bulb.
Hmmm...then you must be thinking of a different solution to this than the one I thought of, and saw elsewhere on the net.... The solution I know doesn't seem applicable to me in the case of the fruit crates.
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Old Feb 28, 2005, 09:14 PM   #9
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Originally Posted by mkrishnan
Hmmm...then you must be thinking of a different solution to this than the one I thought of, and saw elsewhere on the net.... The solution I know doesn't seem applicable to me in the case of the fruit crates.
Come to think of it, you are right, its somewhat different, i guess. Oops
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Old Feb 28, 2005, 09:14 PM   #10
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Quote:
Originally Posted by angelneo
A father who recently died left a will to his 4 sons. the oldest son should get half of his asset, the second son should get a quarter of his asset, the third should get an 1/8 of the asset and the last should get a tenth of the asset. Unfortunately, the father left 39 sheeps to his sons, and the sons brought forth their case to you. How would you solve this?
Can I try? I haven't heard this one before. If you pretend that he had forty sheep, then:

Son 1 -> 20 sheep (1/2), 19 left
Son 2 -> 10 sheep (1/4), 9 left
Son 3 -> 5 sheep (1/8), 4 left
Son 4 -> 4 sheep (1/10), none left.

The secret lies in the fact that 1/2 + 1/4 + 1/8 + 1/10 < 1.

Is that correct?
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Old Feb 28, 2005, 09:16 PM   #11
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Quote:
Originally Posted by angelneo
Come to think of it, you are right, its somewhat different, i guess. Oops
Aww, that's too bad. I was hoping for some really neat answer.
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Old Feb 28, 2005, 09:16 PM   #12
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Quote:
Originally Posted by mkrishnan
Can I try? I haven't heard this one before. If you pretend that he had forty sheep, then:

Son 1 -> 20 sheep (1/2), 19 left
Son 2 -> 10 sheep (1/4), 9 left
Son 3 -> 5 sheep (1/8), 4 left
Son 4 -> 4 sheep (1/10), none left.

The secret lies in the fact that 1/2 + 1/4 + 1/8 + 1/10 < 1.

Is that correct?
yelp. I remember going through this quite sometime ago when I was about 12 and have a hard time solving.
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Old Feb 28, 2005, 09:20 PM   #13
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The boxes had labels identifying what was in them. But, the labels were them scrambled an put on different boxes.
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Old Feb 28, 2005, 09:23 PM   #14
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Quote:
Originally Posted by daveway00
The boxes had labels identifying what was in them. But, the labels were them scrambled an put on different boxes.
I think the idea is that the statement "The labels for the crates have been put on the wrong crates." must be correct in order to solve this.
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Old Feb 28, 2005, 09:24 PM   #15
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Quote:
Originally Posted by angelneo
Since we are on the subject of brain teaser, here's another one. (not sure if you guys have heard this one)

A father who recently died left a will to his 4 sons. the oldest son should get half of his asset, the second son should get a quarter of his asset, the third should get an 1/8 of the asset and the last should get a tenth of the asset. Unfortunately, the father left 39 sheeps to his sons, and the sons brought forth their case to you. How would you solve this?
I can't be very elegant with my solution, I'm afraid..but :

last son - 4 sheep (10% of 40)
3rd son - 5 sheep (1/8 of 40)
2nd son - 10 sheep (25% of 40)
1st son - 20 sheep. (50% of 40)

involves phantom sheep, but otherwise works. Has something to do with 1/8th me thinks, but haven't messed around with math in a while.
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Old Feb 28, 2005, 09:28 PM   #16
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Quote:
Originally Posted by angelneo
I think the idea is that the statement "The labels for the crates have been put on the wrong crates." must be correct in order to solve this.
Only breaks down when the labels are "randomly" placed on the crates -- meaning you don't know if the label is right or wrong until you open them.
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Old Feb 28, 2005, 09:30 PM   #17
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Quote:
Originally Posted by blackfox
I can't be very elegant with my solution, I'm afraid..but :

last son - 4 sheep (10% of 40)
3rd son - 5 sheep (1/8 of 40)
2nd son - 10 sheep (25% of 40)
1st son - 20 sheep. (50% of 40)

involves phantom sheep, but otherwise works. Has something to do with 1/8th me thinks, but haven't messed around with math in a while.
Oh man, this is way too easy for macrumors members
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Old Feb 28, 2005, 09:32 PM   #18
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Quote:
Originally Posted by Sun Baked
Only breaks down when the labels are "randomly" placed on the crates -- meaning you don't know if the label is right or wrong until you open them.
But if the labels are random. What if you open a crate which had the label correct, in spite of the randomness, you wouldn't be able to determine the other 2.
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Old Feb 28, 2005, 09:32 PM   #19
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OK. Lets say that the crates were accurately labeled with what was in the box. Could it be done then?
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Old Feb 28, 2005, 09:34 PM   #20
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Quote:
Originally Posted by daveway00
OK. Lets say that the crates were accurately labeled with what was in the box. Could it be done then?
I think that if you assume that it is possible that any less than all of the crates are mislabelled (i.e. either one of the crates is correctly labelled, or all of them are), that this is not possible.
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Old Feb 28, 2005, 09:35 PM   #21
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Quote:
Originally Posted by angelneo
But if the labels are random. What if you open a crate which had the label correct, in spite of the randomness, you wouldn't be able to determine the other 2.
That's why I said it "breaks down" only under the randomness example.

Quote:
Originally Posted by daveway00
OK. Lets say that the crates were accurately labeled with what was in the box. Could it be done then?
Then why would you open a crate?

Unless you wanted something to eat.
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Old Feb 28, 2005, 09:38 PM   #22
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Originally Posted by Sun Baked
That's why I said it "breaks down" only under the randomness example.

Then why would you open a crate?

Unless you wanted something to eat.
Oops, sorry for my misunderstanding.
talking about fruits and eating is making me hungry for my lunch.
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Old Feb 28, 2005, 09:39 PM   #23
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Quote:
Originally Posted by angelneo
Oops, sorry for my misunderstanding.
talking about fruits and eating is making me hungry for my lunch.
Hey, pass me one of those bananas! Don't hog!

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Old Feb 28, 2005, 09:55 PM   #24
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Quote:
Originally Posted by daveway00
My teacher put a brain teezer out a few days ago and my class thinks it is impossible to figure out.

>>There are 3 crates holding apples and oranges. 1 crate is holding apples. 1 crate is holding oranges. Another crate is holding apples and oranges. The labels for the crates have been put on the wrong crates. You are allowed to open one crate. Which crate do you open to figure out what the other crates have in them? You must only open 1.<<

I'm convinced this is impossible and my teacher is just making a joke out of it.

Open the one with apples and oranges. Then see which is the heavier fruit and you can use that to work out which is in the other crates.

I don't know if that is the offical or clever answer to the puzzle or not but I think it would work in reality.

Edit: if you open a pure (only apples or only oranges) one first then the other pure one will be the one most different in weight, and the mixed one will have the middle weight.

Last edited by broken_keyboard; Feb 28, 2005 at 09:59 PM.
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Old Feb 28, 2005, 10:05 PM   #25
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Originally Posted by broken_keyboard
Open the one with apples and oranges. Then see which is the heavier fruit and you can use that to work out which is in the other crates.
Hmmm...interesting. Assuming that the boxes are packed in a similar enough way, so that the amount of empty space in each box is approximately the same, then this would work. Nice!
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