# Impossible Brain Teezer

#### Daveway

##### macrumors 68040
Original poster
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.

#### mkrishnan

##### Moderator emeritus
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?

#### mkrishnan

##### Moderator emeritus
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.

#### angelneo

##### macrumors 68000
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

#### atszyman

##### macrumors 68020
daveway00 said:
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.

#### Sun Baked

##### macrumors G5
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.

#### angelneo

##### macrumors 68000
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

#### mkrishnan

##### Moderator emeritus
angelneo said:
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.

#### angelneo

##### macrumors 68000
mkrishnan said:
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

#### mkrishnan

##### Moderator emeritus
angelneo said:
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?

#### mkrishnan

##### Moderator emeritus
angelneo said:
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.

#### angelneo

##### macrumors 68000
mkrishnan said:
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.

#### Daveway

##### macrumors 68040
Original poster
The boxes had labels identifying what was in them. But, the labels were them scrambled an put on different boxes.

#### angelneo

##### macrumors 68000
daveway00 said:
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.

#### blackfox

##### macrumors 65816
angelneo said:
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.

#### Sun Baked

##### macrumors G5
angelneo said:
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.

#### angelneo

##### macrumors 68000
blackfox said:
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

#### angelneo

##### macrumors 68000
Sun Baked said:
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.

#### Daveway

##### macrumors 68040
Original poster
OK. Lets say that the crates were accurately labeled with what was in the box. Could it be done then?

#### mkrishnan

##### Moderator emeritus
daveway00 said:
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.

#### Sun Baked

##### macrumors G5
angelneo said:
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.

daveway00 said:
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.

#### angelneo

##### macrumors 68000
Sun Baked said:
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.

#### mkrishnan

##### Moderator emeritus
angelneo said:
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!

#### broken_keyboard

##### macrumors 65816
daveway00 said:
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.

#### mkrishnan

##### Moderator emeritus
broken_keyboard said:
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!