12 balls: The solution.

At least, I think it's a solution. Please have a good, long look at it, figure out what it's talking about and then tell me if I've got anything wrong.

If you haven't had a go yourself, don't look at the image, just go here for the original problem, and here for a clue. It wouldn't be any fun if you went straight for the solution, would it!


The solution
Warning! This is the solution and contains spoilers!

O.k, that's not very easy to read, is it? Might be a good idea to click on it and view it full-size.

Just in case you're not sure what's going on, here's a walk-through of just one of the possibilities to give you an idea:

1. First up, you need to name your balls. I've gone for the rather unimaginative (but not too confusing) 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 & 12. You could go for A-L if you wanted to, or you could think of 12 different names, but then you might get too attached.
2. Weigh* any four balls against any other four. I've gone for 1, 2, 3 & 4 against 5, 6, 7 & 8. Three things can happen here:
   i) The two sets of balls balance;
   ii) The two sets don't balance, with the first set rising and the second falling;
   iii) The two sets don't balance, with the first set falling and the second rising.
   Let's pretend they're balanced:
3. If the two sets are balanced, you know that balls 1 - 8 are fine, and the odd one out is either 9, 10, 11 or 12. To find out which one, first you need to weigh** two of the suspects against one suspect and one fine ball. In my example, I've gone with 9 & 10 against 11 & 1. Again, three things can happen:
   i) The two sets balance;
   ii) The two sets don't balance, with the first set rising;
   iii) The two sets don't balance, with the first set rising.
   Let's pretend they're unbalanced, and that the first set (9 & 10) rise.
4. If 9 & 10 rise, then one of two things is true:
   i) Either 9 or 10 is too light;
   ii) 11 is too heavy.
   To work out which it is, weigh*** the balls in the first set against each other (e.g. 9 against 10). Once more, three things can happen, and the solution depends on which:
   i) The two balls are balanced - in which case, it must be that 11 was the odd one out, and it was too heavy;
   ii) The balls are unbalanced, with 9 rising - in which case, it must be that 9 is odd, and it's too light (as 10 has already been in a rising set, so can't be too heavy);
   iii)The balls are unbalanced, with 10 rising - in which case, it must be that 10 is odd, and it's too light (for similar reasons as in the previous case).

I hope that makes some kind of sense. If not, or if you'd like any parts of my flow chart explaining in greater detail, feel free to get in touch (leave a comment, or send me a message on Twitter (@TeaKayB), or something).

* This is the first weigh.

** This is the second weigh.

*** This is the third weigh.