12 Apples Puzzle

[Gainy]

Thought about putting this in the riddles thread, but it doesn't really suit it.

There are 12 apples, all seem identical. 11 of these apples weigh the same, but the other is a different weight - be that lighter or heavier.
You are given 3 opportunities to weigh these apples (in whatever quantity you see fit) on a set of scales*.
From this you have to deduct which apple weighs differently, and whether it is lighter or heavier than the others.

This is not a trick question, and does have an answer. Please post away!

* By scales, I mean: http://www.ma-strasbourg.justice.fr/images/balance.gif

 

[blackheart]

Eat all of the apples until they all weigh the same

 

[Gainy]

Eating the apples isn't an option Besides that still doesn't answer me question

 

[Warman17]

1) put 6 on one side and 6 on the other.
2) Now using which side is heavier put 3 on one side and 3 on the other.
3) Now using the heavier side put 2 apples o nthe scale, if they're equal the 3rd apple is the heaviest or the one that is heavier is heavier.

Of course this only works if the apples heavier instead of lighter so you got a 50-50 chance of it working.

 

[Gainy]

Sorry but no

You have to be 100% sure that it is going to work else it is wrong, hence your answer is wrong.

 

[Arminius]

Can I use a three-way scale?

 

[Gainy]

No ?

Note:

* By scales, I mean: http://www.ma-strasbourg.justice.fr/images/balance.gif

 

[onejayhawk]

Divide the apples into three groups of four. Weight two groups against each other. If they balance, you are fortunate. Each of these apples is of like weight. Put three of the remaining batch on the scale against three of these. If they balance, the remaining one is the odd one. Weigh it against one of the others to detemine if it is heavy or light. If the second weighing is uneven, then you will know that one of the three is either light or heavy (and which way). waeight two of the the odd batch against each other. You know whether the odd apple is light or heavy, so if they are unbalance it is the one that is lighter or heavier than the other, as appropriate. IF they balance the last one is the odd one.

If the two groups of four are unbalanced, then the third groups is safe. Take one apple from each side and switch them, while replacing the three other apples on one side with safe apples. If the scale is unbalanced in the same direction as before, then one of the three apples which were not moved is the odd one, and light or heavy depending on the direction. determine which as above. Likewise if the scale balances, then one of the three removed from the scale is the odd one, and may be isolated as before. Finally, if the scales move the opposite direction then one of the two which were switched is the odd one. choose the heavier and weigh it against a known apple to determine if it is heavier than all, or the other is lighter than all.

J

 

[Gogf]

I'm close.

1. Six on one side, six on the other.
2. Break the heavier side up into 3 and 3. If they're even, put them both aside, and look at what was lighter. If they're no easier, put the lighter side in step one aside, and the lighter side in this one aside, and procede to step three.
3. Put two on the scale (on opposite sides), and one off. If they're not even, the heavier one is the heavier apple. If they are equal, the other one is the heavier apple.

I don't know what to do if the two three from the heavier side are equal though. Not sure how to find it in the six from the lighter side with one weigh (there must be a better way to do #2).

 

[onejayhawk]

I'm close.

1. Six on one side, six on the other.
2. Break the heavier side up into 3 and 3. If they're even, put them both aside, and look at what was lighter. If they're no easier, put the lighter side in step one aside, and the lighter side in this one aside, and procede to step three.
3. Put two on the scale (on opposite sides), and one off. If they're not even, the heavier one is the heavier apple. If they are equal, the other one is the heavier apple.

I don't know what to do if the two three from the heavier side are equal though. Not sure how to find it in the six from the lighter side with one weigh (there must be a better way to do #2).

This requires at least 4 measurements if the scales balance the second weighing. The actual method is pretty convoluted.

J

 

[Gainy]

Right on J

You've either heard it before, or you are just really clever

Ask your friends this one though, even though it seems simple enough it is actually pretty difficult! (btw gogf yer wrong as you kinda noticed)

 

[Gogf]

This requires at least 4 measurements if the scales balance the second weighing. The actual method is pretty convoluted.

J

Ah. Crossposted with you earlier. Very interesting way to do it!

 

[Tomoyo]

Are you allow to use your hand to balance the apples?

 

[Gainy]

I don't see why not. But that will not affect the actual weight of the apples, just your perception of it.
So whatever answer you would get would probably be wrong.

It is not a trick question of any sort, just use simple un-adulterated weighing methods. IE stick the apples on the scales...

 

[Xen]

If one wanted to be an *Crap-head* about it, I woudl say that one shoudl refuse to weigh the appels on religious principles.

 

[Syterion]

What do you mean not fitting in the puzzle thread? That puzzle has already been in both puzzle threads. But luckily for you I won't spoil it.

 

[Erik Mesoy]

You can find one of 27 apples this way, actually.

 

[Timko]

Look at the puzzle quiz thread. You can't do 27 unless you know whether the odd one out is heavy or light. You can do 13 if all you want is the odd one out (ie you would know which is wrong but not know if it is heavy or light), and if you happen to have a spare extra apple which you know is right then you can do 14.

 

[Gainy]

What do you mean not fitting in the puzzle thread? That puzzle has already been in both puzzle threads. But luckily for you I won't spoil it.

My bad
The first post shows fairly simple 'riddles', which have no specific answer. I assumed that's what the rest of the thread contained -- and I wasn't going to read through 200 other posts just to be sure

Might as well lock this one then.

 

[Yaniv]

Right on J

You've either heard it before, or you are just really clever

Ask your friends this one though, even though it seems simple enough it is actually pretty difficult! (btw gogf yer wrong as you kinda noticed)

Although I was too late in posting the solution, I did solve this riddle once. Took me several hours though- I was 13, it was summer break, and I had no life (Not tha I do now). Any way, you don't have to clever to solve this- I'm an idiot and I did