Balance problem

I have been given a balance which can weight which one of two given
sets of balls is heavier than another or are they as heavy. We have
been given a set A of balls, |A| <= (3^n-1)/2 with one ball has a
different weight from the others.

Prove that if I can use a balance n times, I can find the ball which
has a different weight from the others. Prove that if |A| = (3^n-1)/2,
we can't necessary find the ball which has a different weight from the
others by using a balance n-1 times.

.

Relevant Pages

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