The Gold Coin Test
Your eccentric Uncle Jake is a rare coin collector. He has
twenty-four coins that appear identical, except only one is solid
gold; the others are made of a heavier alloy. He sits you in front
of a balance and says you can have the gold coin if you can find
it. You can use the scale only three times. How can you find the
lightest coin?
Since the Gold coin is the lightest, all the other coins are
made of highly toxic, radio-active heavy metals. To find the gold
coin:
1. Jake should divide the coins into two piles of 12 coins. The
pile with all alloy coins will be at critical mass, and will
enter a chain reaction, annihilating itself.
2. Take the remaining pile, and divide it into two piles of 6
coins. Place the piles on opposite sides of the scales. The
scales have thus been used for the first time. The heavier
pile will be hottest, and will melt through the scale pan
beneath it.
3. Take the pile of 6 coins in the remaining scale pan, and
divide into two groups of 3 coins. Uncle Jake should keep one
pile himself, and give one to you. Instruct Uncle Jake to
place one coin in each hand, while placing one under his
tongue. Wait for a response. At this point, Uncle jake is
either:
a. Dead with the gold coin in his left hand,
b. Dead with the gold coin in his right hand,
c. Dead and you have the gold coin, or
d. Alive with the gold coin in his mouth.
Now precede accordingly...
4. (a, b, and c) To ascertain which is the case, place the
discarded pile of 6 coins (hopefully, you have been quick, and
the pile will only have melted through the table and not the
floor), and melt a hole in the intact scale pan with them.
Now the scale pans have the same mass. Place the coin from
Uncle Jake's left hand in the left scale pan, and the coin
from his left hand in the right scale pan. If the balance is
level, then you have the gold coin. If the balance is heavier
on one side, take the coin from the other side - that is the
gold coin, continue to step 5.
So YOU have the gold coin. Put one coin in each of Uncle
Jake's hands. Now repeat step 4, disregarding the need to
remelt the scale pans, and precede to step 5 regardless.
It can be proven that this step iterates at most twice,
so this step may use the scales for the SECOND and THIRD
times.
(d) Beat Uncle Jake over the head with the scales, which are,
after all particularly strong - enough to support these extra-heavy coins. This uses the scales for the SECOND time. Take
the Gold coin from Uncle Jake's Mouth.
5. Get all of the coins and pile them on Uncle Jake's Body. The
evidence of Uncle Jake's existence should disappear in a few
minutes. The coins will take somewhat longer. See World
Book, "Half-Life". As Jake said, "You can have the gold coin
if you can find it." Well... You found it!