Let us denote the coins
by C1, C2, .... , C108. Make 12 groups each containing 9 coins. The groups
can be denoted by (C1, C2, .... , C9), (C10, C11, ..... , C18), ..... ,
(C99, C100, .... , C108).
Following the procedure
of the first problem, get the defective group and its defect . Let the
group be (C1, C2, ... , C9) and let one coin in it be heavy. Make 3 equal
subgroups of this group. The subgroups are (C1, C2, C3), (C4, C5, C6) and
(C7, C8, C9). Put (C1, C2, C3) in P1 and (C4, C5, C6) in P2. We have following
cases.
Case-1:
P1 goes down.
Now we know that one of
C1, C2 and C3 is heavy.
Case-2:
P2 goes down.
Now we know that one of
C4, C5 and C6 is heavy.
Case-3:
They balance each other.
Now we know that one of
C7, C8 and C9 is heavy.
In all the 3 cases follow the procedure of problem-3 and get the heavy coin.
Now go for problem-1.