Re: Tough brainteaser.
 

You are wrong.
I'll elobarate.
Say you weigh AB v CD and they balance.
So the outlier is E,F,G or H.
According to your theory you now wiegh
AB v EF.
And if they balance they G or H must be the outlier.
Now you weigh G against A. If they balance, then H must be the outlier. But you don't know if H is ligther of heavier than the others.
You are close, but sadly no cigar.

Re: Tough brainteaser.
 

Ok I see your point I'll try again...

1) First step as above to narrow the field four balls- A, B, C and D and four 'normal' balls N,N,N,N.

2) Weigh A, B, and C against 3 normal balls (!)
If they are equal, D is the outlier and you use the last weighing to work out if it heavier or lighter than a normal ball.

If they dont match, you know the outlier is A, B, or C ALSO you KNOW IF IT IS HEAVIER/LIGHTER THAN NORMAL!

3) Now, for the third weighing, weigh A vs B. If they are equal C is the outlier (and you know the mass). If they are unequal, because you know the mass difference of the outlier, you can identifier the outlier between A and B.

Hows that?
aquifex