You are given 12 gold coins, however, you are later told that 1 of
the 12 coins is a fake. The only way of discerning the fake coin
from the real ones is by it's weight. All of the 11 real gold coins
will weigh exactly the same amount each, while the fake coin will
weigh EITHER more or less than each other coin.
The only tool you have available to you is a balance. This works
simply by placing some coins on the left and right "pans" of the
balance, and then activating the balance. Upon activation, the
balance will simply state whether the left pan's contents are heavier,
the right pan's contents are heavier, or they are equal in weight.
What is the minimum number of times you will need to activate the
balance (and how would you do it) to determine:
- Which coin is the fake and
- Is the fake coin heavier or lighter than the rest?