> > You have twelve marbles and a balancing scale.
> >
> > You know that one of the marbles has a different
> > weight than the other eleven.
> >
> > Your job is to find this marble, and to find out if it's
> > heavier or lighter than the others.
> >
> > What's the minimum number of weighings required?
>
> I would think 3...
>
> 1- 4 on one side, 4 on other side, 4 no where
>
> 2- 2 on each side
>
> 3- 1 on each side
>
> Jimmy O"But then again, i'm an idiot."f York

It is three. I love this problem. It's a fairly complicated system, and I know there is more than one solution.

To begin: 4 on one side, 4 on the other, 4 on the table.

1) If both sides are equal, put 3 of the 4 from the table onto one side and 3 from the eliminated batch on the other.

A) If both sides are equal, weigh the last marble against another marble and see whether it's lighter or heavier.

B) If the side with the marbles still under consideration moves up or down, put 1 of those marbles on one side and 1 on the other.

i) If both sides are equal, the odd marble out is the different one, and it is either lighter or heavier depending on whether the 3 marbles moved up or down, respectively.

i) Whichever side moves (up or down) in the same direction that the three did earlier, that is the unique marble. The weight difference should be plain from that same weighing.

2) If, in the first weighing, the scale moves, it gets more confusing. Sorry. Take 1 marble from each side and switch their places. On one side, remove the other 3 and set them aside separately. Replace them with three duds from the 4 originally left out.

A) If the two sides are now equal, the different marble is among the 3 you just removed. You should remember whether it went up or down. Weigh one against another.

i) If both are equal, it's the marble from that 3 which is still on the table.

ii) If they aren't equal, it's whichever marble went the same direction as it did in the first weighing.

B) If the two sides switched directions--the side that went up now goes down and vice versa--the marble you want is one of the two you switched places. Weigh one against a normal marble.

i) If both sides are equal, the special marble is the one left out. It's heavier or lighter depending on which way it moved when it was weighed in group earlier.

ii) If the sides move, the marble in question is either lighter or heavier, depending on the same thing as has been explained several times.

C) If the two sides are still uneven with the same sides going up and down as before, the suspect marble is among the three that haven't been moved from their side. Weigh one against another.

i) If they're equal, the marble you want is the one that didn't get weighed this last time, and is either lighter or heavier depending on how it moved earlier.

ii) If the sides moved, the special marble is the one that moved the same direction as it did the first two times. You should be able to tell the weight difference.

Well, that's the key. I hope you can understand what I meant.

gab"It would read so much easier if I could indent."by