The Disconcerted Crooks Quest

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Standard Information

Issam and his merry band of crooks have outsmarted themselves. Find them and help them out with their problem.

   Estimated Mental Difficulty Rating:   Eight
   Estimated Physical Difficulty Rating: Zero
   Estimated Danger Rating:              Five

   This quest was created by Ishamael.

Starts at Grey Mouser. "say crooks" then after some dialog "say password." Next go n of where the catelius minor quest is (the dirty alley). Knock on door. Say the password. Then follow their instructions. Kachan says, "The keys are magically enchanted. At any particular time, only one key is the correct key. The problem is that the key that is correct one time may not be correct the next. The correct key will be either slightly lighter or slightly heavier than the others. That's why we stole the balance."

Kachan says, "We stole this chest only to discover that it was magically trapped. I have been able to determine that the chest will, in all likelihood, explode if it is opened incorrectly, which will ruin the contents. These twelve keys are the keys that open the chest. Rather, one of these keys opens the chest."

Kachan says, "The keys are magically enchanted. At any particular time, only one key is the correct key. The problem is that the key that is correct one time may not be correct the next. The correct key will be either slightly lighter or slightly heavier than the others. That's why we stole the balance."

Kachan says, "Unfortunately, the balance will only work three times in any given time frame. By the time the balance works again, the keys have changed and we have to start over. What we need you to do is figure out how to determine which of the twelve is the correct key using only three weighings on the balance. If you can do that, and use that key to open the chest, you will be handsomely rewarded. However, if you fail and waste another chance at the balance, my comrades will be most displeased."

Kachan says, "If you're willing to give it a try, here are the commands to get the balance to work. You can put XXX in left/right pan and get XXX from left/right pan. You must secure balance before you can put items into or take items out of the pans. When you are ready, simply weigh balance to see which pan is heavier or if they are balanced."

Once you think you have the correct key "unlock chest with key."

Tips:

• My strategy was to put half in one pan then half in the other and weigh. I took the lighter half and dropped them. Then I put half of the remaining six on each side and dropped the lighter side. Then I put 1 key on the left and 1 on the right. If the scale was balanced, I had the heavy key in my hand. If it tilted to one side then that was the key. It says the key can also be lighter in which case I would've had to have done the opposite but I don't think there's any way to tell going in so there's still a little luck involved. (Just tested, it isnt always the light blue key)

Quebond's Notes:  It's more deterministic than that if you use the 3 balances effectively.
The temptation is  to do what is said above, and weigh all 12 at once.  However, we know we have 3
opportunities, and if you half  12 3 times, 12 -> 6 -> 3.  However, you really have *3* states to use,
using them all is the key (pun  intended).  Split the 12 into 3 groups, not 2 - weigh 4 on one side, 4
on the other, and keep 4 out.  If you need more help from there, see: 
http://www.mathsisfun.com/pool_balls_solution.html

• If you're relatively low level and may not want to risk blowing your hand off, kill the thieves one at a time (Kachan, in particular) before the third weighing. That way you can leave without aggroing them all, if your third attempt doesn't turn up the correct key.

//Follow this// Solution from Turok:

For simplicity I'm going to call the keys A-L

1) Put ABCD into left and EFGH into the right pan and weigh them

2) If they are equal

 A) take EFGH out of the right and D key out of the left.
 B) put IJK into the right, do 2nd weighing
 C) If they are equal the key to unlock the chest is L
 D) If they were unequal, make note of if the right side was heavier or lighter
   1) remove ABC from the left and IJ from the right, put J into the left, 3rd weighing
   2) if they are equal, the key to unlock the chest is I
   3) if they are unequal, the key to unlock is the key that is heavier/lighter depending on step D above (J or K)

3) If they are unequal, make note of which side was heavier or lighter

 A) set up the pans so AFGH is in the left and EIJK is in the right, do 2nd weighing
 B) If they are equal
   1) Remove all keys from both pans, B into the right pan and C into the left pan, do 3rd weighing
   2) If they are equal, D is the key to unlock the chest
   3) If they are unequal, the key to unlock is the side that is heavier/lighter based on what you noted in 3 above (B or C)
 C) If they are unequal, make note of if it changed which side is heavier or not.
 D) If the side that was heavier did not change
   1) set up the weighing with AE in the left pan and JK in the right.  Do 3rd weighing.
   2) if the side that was heavier does not change the key to unlock is A
   3) if the side that was heavier changed, the key to unlock is E
 E) If the side that was heavier did change
   1) set up the weighing with F in the left, G in the right, do 3rd weighing
   2) If they are equal, H is the key to unlock
   3) If they are unequal
     A) if the left pan was heavier in A above, it is the key that is heavier, if the left pan was lighter in A above, it is the 
        key that is ligher (F or G)

If this is confusing, and I'm in game, just ask me and I'll tell you what to do.