Prove using induction:Suppose you have a group of plates where exactly one of them is heavier than the others while others weigh

the same. The plates are otherwise identical. You wish to find the heavier plate by using a balance; you may

place an arbitrarily$-$large stack of plates on each side of the balance. Prove by induction: Given a group of

$3^n$ plates, the heavier one can be found using a balance and with only $n$ weighings.