Process To Identify Fake Coin
What was the task given?
If we knew, the fake coin is lighter or heavier than original one then the process would have been pretty simple like this! But we don't know.
Let's number the coins from 1 to 12. We'll make 3 groups of these coins as 1,2,3,4 in one group, 5,6,7,8 in other group and 9,10,11,12 in one more group.
First of all weigh 1,2,3,4 against 5,6,7,8.
CASE 1 : 1,2,3,4 = 5,6,7,8
That means coin among 9,10,11,12 is fake one. So weigh 9,10 against 11,8.
CASE 1.1 : If 9,10 = 11,8 then 12 is fake coin.
CASE 1.2 : If 9,10 > 11,8 then either 9 or 10 is heavier (hence fake) or 11 is lighter (hence fake). Weigh 9 against 10. If they balance then 11 is fake one. If they don't then heavier of 9 & 10 is fake.
CASE 1.3 : If 9,10 < 11,8 then either 9 or 10 is lighter (hence fake) or 11 is heavier (hence fake). Weigh 9 against 10. If they balance then 11 is fake one. If they don't then lighter of 9 & 10 is fake.