Much much tougher brain teaser

[milliondollaz]

if you know if it's heavier or lighter...

1. you split the group into two and weigh (compare) them.
2. if odd stone is heavier, you take the heavier 6, if it's lighter, you take the lighter 6, and split them into two groups of three, and weigh them.
3. you take the three stones that are heavier (lighter) and you weigh just two of them.

it will be obvious if one is heavier (lighter). if they balance, the one in your hand is heavier (lighter).

still can't figure out how to do it if you don't know if it's supposed to be heavier or lighter. cause you could get the first step wrong and split up a group of evenly weighing stones, and you would need another step fix your wrong initial guess...

[Klepton]

6 on each side = take 6 rocks from heavier side
3 on each side = take 3 rocks from heavier side
put any 2 on the scale = if one is heavier, thats the one, if they weigh the same, one not on scale is

oh...dammit i wrote this and didn't see heavier OR lighter.

oh well i got it if it was heavier

[yellowjack]

Based on my attempts and other replies w/ similar results, I'm beginning to think this was one cruel post.

[chuddo]

this puzzle is only solvable in 3 steps when using a balance scale.

and it is not too tough, but a bit fun.

separate into 3 piles of 4 rocks: A, B, and C

assume odd rock is light.

Place A and B on the balance. if balance = even, odd rock is in pile C. if uneven, odd rock is obviously on the lighter scale.

you now have a group of 4 rocks and one is odd, and can use the balance scale two more times.

Seperate this group of 4 into 2 groups of 2 stones: D and E.

again, lighter side contains the odd rock.

finally take these last 2 rocks, balance them on the scale. lighter rock is obviously the odd rock of the 12.

[Stuey]

3 groups of 4 rocks is right
if they don't weigh the same or in the case of the type of scale I am using "balance" I remove 2 rocks from each side at the same time.

If that causes the scale to balance then I know I got the bad one in one of my mitts.

If the scale stays put then I can use the 4 stones I pulled as standard weighing ones to eliminate the remaining 4 on the scale with the previous method.

Basically I am cheating and using the scale more than 3 times but it does not apear that way as I am just removing the rocks in a certian order to help my deductions.

Makes sence to me but I describe it badly.

[battschr]

[ QUOTE ]
this puzzle is only solvable in 3 steps when using a balance scale.

and it is not too tough, but a bit fun.

separate into 3 piles of 4 rocks: A, B, and C

assume odd rock is light.

Place A and B on the balance. if balance = even, odd rock is in pile C. if uneven, odd rock is obviously on the lighter scale.

you now have a group of 4 rocks and one is odd, and can use the balance scale two more times.

Seperate this group of 4 into 2 groups of 2 stones: D and E.

again, lighter side contains the odd rock.

finally take these last 2 rocks, balance them on the scale. lighter rock is obviously the odd rock of the 12.

[/ QUOTE ]
Why can we assume that the odd rock is light?

[Luzion]

[ QUOTE ]
this puzzle is only solvable in 3 steps when using a balance scale.

and it is not too tough, but a bit fun.

separate into 3 piles of 4 rocks: A, B, and C

assume odd rock is light.

Place A and B on the balance. if balance = even, odd rock is in pile C. if uneven, odd rock is obviously on the lighter scale.

you now have a group of 4 rocks and one is odd, and can use the balance scale two more times.

Seperate this group of 4 into 2 groups of 2 stones: D and E.

again, lighter side contains the odd rock.

finally take these last 2 rocks, balance them on the scale. lighter rock is obviously the odd rock of the 12.

[/ QUOTE ]

What the hell man... the hard thing about this puzzle is NOT KNOWING if the rock is gonna be heavier or lighter then the other 11 rocks...

Anyone couldve solved it if we already knew ahead of time if the rock was heavier or lighter then the other rocks

[chuddo]

blah, im a donkey. didn't take note of the fact you have to devine whether or not the stone is lighter or heavier relative to the other stones while finguring it out.

this makes the problem much more challenging, but you can see that the partial algorithm in my last post is a piece of it.

i just worked it out and now think this is a good puzzle, and will leave the final solution out so others can work it out.

[Stuey]

[ QUOTE ]
3 groups of 4 rocks is right
if they don't weigh the same or in the case of the type of scale I am using "balance" I remove 2 rocks from each side at the same time.

If that causes the scale to balance then I know I got the bad one in one of my mitts.

If the scale stays put then I can use the 4 stones I pulled as standard weighing ones to eliminate the remaining 4 on the scale with the previous method.

Basically I am cheating and using the scale more than 3 times but it does not apear that way as I am just removing the rocks in a certian order to help my deductions.

Makes sence to me but I describe it badly.

[/ QUOTE ]

Am I wrong? here is a longer version

Separate the rocks into 3 equal piles of 4.

Step 1

Put any 2 piles on a balance type scale, if they balance the 3rd pile has rock X in it. And you can use any 2 rocks on the scale as standard weight rocks to find out where X is in the remaining 4 using step 2 below.

If they don’t balance remove 2 from each side at the same time. If that makes it balance then you know you are holding rock x and all other rocks are standard weight so you can use them to find which of the 4 in your hands is X easily with step 2.

If it does not balance when you remove 2 from each side you know rock x is on the scale and all other rocks are standard and you can use step 2 to find it.

It will look like you only use the scale 1 time but you actually use it 2 times as you remove the rocks in a certain order in the case when it does not balance on the first test. It is a cheat but you gota live!

Step 2

Now that you know which group of 4 rocks x is in just take 2 from that pile and weigh them vs 2 standard ones. If it balances take 2 of the remaining ones and weight it vs 2 standard ones and you will have found it. Just remove one of the rocks and watch the scale to find out which is X and if it is heavy or light based on the scale reaction. Then say I hold X and it is heavy or light or say rock X is on the scale and it is heavy or light whatever the case might be.

You only need to use the scale twice in all possible combinations once you narrow it down to 4 rocks and you have 2 standard ones to use. You have to pull the trick from step one here again to find out if the rock is heavy or light though but it will look like you only used the scale twice. The trick is watching what happens when you remove one rock from each side.

[deadmoney98]

[ QUOTE ]
Separate the rocks into 3 equal piles of 4. Weigh each, the odd one out contains the different rock (rock X). This also will tell you if it is lighter or heavier and the weight of each individual other rock (Y).

Take two rocks from the group you now know contains rock X and weigh them. If they weigh 2Y, take one of the two remaining rocks and weigh it. It is either X or a Y.

If they don't weigh 2Y, pick one and weigh. It is either X or a Y.

Obviously if the rock weighs Y, the other rock is X and vice versa.

[/ QUOTE ]

[ QUOTE ]
that's more than 3. that's like 5.

[/ QUOTE ]

Wow, I am dumb at 4 AM, sorry about being an idiot.