6. You have n>2 identical-looking coins and a two-pan balance scale with no weights. One of the coins is a fake, but you do not know whether is is lighter or heavier than the genuine coins, which all...

6. You have n>2 identical-looking coins and a two-pan balance scale with no weights. One of the coins is a fake, but you do not know whether is is lighter or heavier than the genuine coins, which all weight the same. Design a T(1) algorithm to determine whether the fake coin is lighter or heavier than the others.