Much much tougher brain teaser

[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.

[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.

[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.

[PorscheNGuns]

Getting closer, but by removing a rock at the end you are essentially using the scale 4 times, making your solution wrong.

-Matt

[ptmusic]

Ok, the way I solved this was to use Scenarios for each possible outcome.

Step 1 always starts the same for each Scenario; Steps 2 and 3 vary depending on the result of Step 1.

I am calling the rocks by number 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

SCENARIO A

Step 1: 1,2,3,4 vs. 5,6,7,8. They are equal.

Step 2: 1,2,3 vs. 9,10,11. They are equal

Step 3: 1 vs. 12. 12 is the odd rock, and it is heavy or light depending on how it weighs against 1.



SCENARIO B:

Step 1: 1,2,3,4 vs. 5,6,7,8. They are equal.

Step 2: 1,2,3 vs. 9,10,11. They are NOT equal. Odd rock is 9, 10, or 11; you know if odd rock is heavy or light now, depending on how this group weighed against 1,2,3.

Step 3a: 9 vs. 10. They are Equal. Odd rock is 11.
Step 3b: 9 vs. 10. They are NOT equal. Odd rock is the heavier rock of the two, if group was heavier in Step 2, or odd rock is the lighter rock if the group was lighter in Step 2.



SCENARIO C:

Step 1: 1,2,3,4 vs. 5,6,7,8. They are NOT equal. Call 1,2,3,4 the side that was lighter. You know the odd rock is one of these 8 rocks. You also know that if it is 1,2,3, or 4 then it is lighter; if it 5,6,7, or 8 then it is heavier. You also know that it is not 9,10,11, or 12.

Step 2: 1,8,9,10,11 vs. 2,3,5,6,12. They are equal. You know that odd is 4 (and light) or 7 (and heavy).

Step 3a: 12 vs. 4. They are equal. 7 is the odd rock and it is heavy.
Step 3b: 12 vs. 4. They are NOT equal. 4 is the odd rock and it is light.



SCENARIO D:

Step 1: 1,2,3,4 vs. 5,6,7,8. They are NOT equal. You know the same information as in Scenario C.

Step 2: 1,8,9,10,11 vs. 2,3,5,6,12. They are NOT equal. If the first group is heavier, 8 is odd rock and it is heavy OR 2 or 3 is odd and light. Go to Step 3a. If 2nd group is heavy, 5 or 6 is odd OR 1 is light; go to Step 3b.

Step 3a: 2 vs. 3. If equal, then 8 is odd rock and heavy. If Not equal, then the lighter of the two is the odd rock.

Step 3b: 5 vs. 6. If equal, then 1 is odd rock and light. If NOT equal, the heavier of the two is the odd rock.


-ptmusic

[sirio11]

Beautiful !

[Matty]

well done

[PorscheNGuns]

-Matt

[ptmusic]

[ QUOTE ]


-Matt

[/ QUOTE ]

Thanks for the photo. It almost makes up for the hour I lost working that one out and trying to put it into words!

-ptmusic