#1. 6 - 6

from the lighter 6 take 4 and keep the other 2 handy.

#2 2 - 2

if one is lighter weigh those two to find out which is lighter.

if both the same, weigh the two that you didn't weigh and the weigh those.

Sheldon, you're assuming that the odd ball bearing is lighter than the rest. The riddle states that you have no idea whether it's lighter or heavier.

Sheldon, your solution will not work, since you don't know if the odd one out is heavier or lighter- just that it's a different weight.

I posted this and another puzzle a while back: http://www.livejournal.com/users/danieljohn/8595.html

It took me a while to solve, but I know one person that solved it in minutes :(

Argh, this is actually much harder than I first thought... everytime I think I have the answer it falls short because I don't know if the odd-ball-out is heavier or lighter...

Maybe that's why I didn't do too well in Physics.

I'm going to leave some of my work out so this isn't a really long comment, but the basic answer is:

#1 4 - 4, leave 4 out

if they balance, then the oddball is one of the four you left out, and the remaining weighings are 2 vs. 2 and 1 vs. 1

if they don't balance then #2 remove 3 from the high side of the balance and put aside, take three from the lower side and move them to the high side and put three from your control (the 4 you set aside) and add them to the low side.

If they scales don't move, then the oddball is one of the 2 balls that you didn't move, either high side or low side, you can then weigh one against a control and determine which one is the oddball.

If the scales equalize then the oddball is one of the 3 you removed from the high side and it is light. Weigh 1 v 1 from that group and you can tell which one is the oddball

If the scales shift low to high, then the oddball is in the 3 that you moved from the low side to the high side, and it is heavy. Again weigh 1 v 1 to determine which one is the oddball.

It took me about 2 hours to realize that weighing 6 v 6 was a dead end. Once I thought of moving from one side to the other, it all came.

Sorry, I meant weighing 3 v 3 (to determine which 6 of the 12 had the oddball) was a dead end. There's absolutely no point in weighing 6 v 6.

What about this?

1) Weigh 6 v. 6 - keep lighter half
2) Weigh 3 v. 3 - keep lighter half
3) Weigh any two. If same, odd man out is light one, otherwise pick the lighter one.

Very easy... took me about 5 mins. The key is to see at what point picking half fails to provide enough information.

Of course, my solution won't work because I misread the problem.

Heh.

My face is red. I didn't realize you didn't know whether the different one was lighter or heavier. Oops.

Haven't quite figured it all out yet, but i do know that the first step is to assign all twelve a variable. I used up and down. then you pick eight and weigh 4 and 4. once you have those you no longer need the four that were not weighed. Now here is where i get stuck cuz i don't know what to do next.