We should devide the 12 coins into three groups, 5,5,and 2
1- for the first five, we weigh 2 against 2, leaving one coin aside.
a- if they are blanced,we put them aside.
b.- if they areĀ“nt balanced.
we should weigh the heavier two with any other two coins :- now... if they balanced so the counterfeit coin is one of the two light coins,which will be easy to be find with the third weigh.....and if they are heavier,then we should weigh them one against one,,,and they heavier is the counterfeit coin.
2- for the 2nd five .we will do the same 2 against 2,leaving one coin aside:-
a- if they are balanced, so one of the two coins left aside is the counterfeit coin, which will be easy to find with the 3rd weigh.
b- if they are not balanced....see above.