>>You have 12 billiard balls. All but one of the billiard balls are of equal weight. The one odd bal :) is either lighter or heavier. You do not know which. You have 3 (balance) scale weighings to determine not only which ball is the odd one but also whether it is lighter or heavier. You must be able to give logic for all possibilies.
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>>Good Luck. :)
>


Gerald is the winner. Cetin also has a correct response, but Gerald has the most unique response, one that I have never seen before. ( and also with fewer balls on the second weighing. )

The key is to divide the 12 balls into 3 groups of 4 then weigh 2 groups against each other. Namely A, B, C. If you weigh A vs B and they are equal you are the rest is fairly simple. The complication comes when A # B either lighter or heavier. Then you must weigh 5 of the unequal balls against each other. In all cases you must have only 3 unknown balls left. Hence using Gerald's syntax I will show you another possibility. ( Group A (1,2,3,4) is lighter than Group B (5,6,7,8) ). 2nd weighing. l1, l2, l3, h5 vs l4, E9, E10, E11. Once again this limits the unknown balls to 3.

If 2nd weighing =.

Weigh h6 vs h7. If # then the heavier is the winner. If = then h8 is the winner.

If 2nd weighing l1,l2,l3,h5 lighter.

Weigh l1 vs l2. If # then lighter is the winner. If = then l3 is the winner.

If 2nd weighing l1,l2,l3,h5 heavier.

Weigh h5 vs E9. If # then 5 is winner.
If = then l4 is winner.

Thanks all for participating.