Welcome to the forum! That is a solution!

]]>(1) 3

(2)3

(3)3

(4) 3

1) (1) vs (2) - if equal weight

(1) vs (3) - from this attemp you will find which has the odd one and you will find in which group that odd one is

Now you got one group having 3 balls..in which the odd ball is

now 1 ball vs 1 ball ...solution found in 3 attempts

the problem with this solution is the rules of inference cannot be observed so clearly as in the ``classical'' solution. it would be quite good if someone (the author?) explained what is the rule of putting the balls on the left and on the right throughout the 3 weightings.

]]>Or isn't it meant to stand for anything?

]]>That is a good solution, and would look good on TV, I reckon.

Hero says "you are going to weigh each one? Harumph!" *throws four on one side, four on the other* *switches a few balls around* "switches one more time* "Here- this one!"

]]>I figured out a solution several months ago, although less nimble but...I tried my best :

Weigh (1st time) 4 balls against other 4 (choose randomly).

IF THE SCALE NOT BALANCED: the last 4 balls (not on the scale) are normal ones.

Name the 4 balls on heavier side A,B,C,D. If the odd ball is in group ABCD, it must be heavier than normal one.

Name the 4 balls on lighter side E,F,G,H. If the odd ball is in group EFGH, it must be lighter than normal one.

Weigh (2nd time) : (N is a normal ball)

A B N ~ C D E

1a/ If ABN = CDE : the odd ball is in group F,G,H.

Weigh F against G (3rd time):

If not balanced, the lighter one is the odd ball.

If balanced, H is the odd ball (and is lighter).

1b/ If ABN ≠ CDE :

1b1/ If the scale tipped towards A,B,N side (heavier): the odd ball is in group A,B,E.

Weigh A against B (3rd time) :

If not balanced, the heavier one is the odd ball.

If balanced, E is the odd ball and lighter.

1b2/ If the scale tipped towards C,D,E side : the odd ball is in group C,D.

Weigh C against D. The heavier one is the odd ball.

IF THE SCALE BALANCED (at the 1st weighing) : these 8 balls are normal ones.

Name the last 4 balls A,B,C,D.

Weigh (2nd time) :

A N ~ C D

1a/ If not balanced (AN≠ CD) : the odd ball is in group A,C,D.

1a1/ If the scale tipped towards A,N side :

If the odd ball is A, it must be heavier than normal one. If the odd ball is C or D, it must be lighter than normal one.

Weigh C against D (3rd time):

If not balanced, the lighter one is the odd ball.

If balanced, A is the odd ball and heavier.

1a2/ If the scale tipped towards C,D side :

If the odd ball is A, it must be lighter than normal one. If the odd ball is C or D, it must be heavier than normal one.

Weigh C against D (3rd time) :

If not balanced, the heavier one is the odd ball.

If balanced, A is the odd bal and lighter.

1b/ If balanced (AN=CD) : B is the odd ball.

Weigh B against a normal ball to know if it is lighter or heavier than normal one .