ok... its a long one tho
place 4 balls on each side, and leave 4 balls behind
the scale will be either even (a) or unballanced (b)
FOR (a):
for (a) remove balls on scale and place 3 of the 4 remaining on one side and 3 of the previously used balls on the other they will either be even (a1) or unballanced (a2)
for (a1) remove balls on scale and place the remaining ball (odd one out) on one side and one of the other balls on the other side to find if it is heavier or lighter
for (a2) with the 3 balls just placed (one of which is the odd one out), place 1 one each side of the scales (giving one ball left over) they will either be even (a21) or unballanced (a22)
for (a21) the remaining ball is the odd one out, place it on the scales with another ball to find if it is heavier or lighter
for (a22) one of those balls is the odd one. remove the heavier ball and replace it with the ball left over, if the scales are still uneven then the lighter of the two balls is the odd one and it is lighter than the rest, if they are even then the ball previously removed is the odd one and is heavier than the rest of them
FOR (b):
for (b) remove 3 balls from each plate. place the 3 removed from the heavy plate onto the light plate and place 3 normal balls (from step 1 the ones left over) and place them on the light plate. the plates will either remain the same (b1), become even (b2) or tip the other way (b3)
for (b1) remove the balls that have just been placed as the odd ball is one of the ones that remained in its place, remove the heavier ball and comparethe lighter one with a normal (one that is of equal weight to the others) ball, if it is even then the ball removed is the odd one and it is heavier. if it is still unbalanced then the odd ball on the scales is the lighter one
for (b2) one of the 3 balls removed is the odd one out. from the previous weigh-in it can be seen that this group contains a lighter ball. place 1 of these 3 on each side of the scale, if it is even then the odd ball out is the one remaining and it is lighter, if it is unbalanced then the lighter of the 2 balls is the odd one out
for (b3) the odd ball is amongst the 3 balls moved from one plate to the other. it can also be seen from the previous weigh-in that the odd ball is heavier than the rest. place 1 of these 3 on each side of the scale, if it is even then the odd ball out is the one remaining and it is heavier, if it is unbalanced then the heavier of the 2 balls is the odd one out.
sorry i joined steps 2 and 3 for part b... it was just dragging onn tooooooo much for me.
now... that better be one fuking big star and it better be 21ct
-dee