12 Gold Coins, 1 is Fake. Use a Balance to Discover Which
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?
5 Pirates, Voting to Split 100 Gold Pieces
You are the eldest of 5 pirates, and fortune be with you, you discovered
buried treasure of 100 gold pieces.
Being the oldest pirate, you get to decide how much each pirate's share will
be. However, once you've laid out your plan, stating how much each pirate
will get out of the 100, the 5 of you will take a vote as to whether
they like the plan (your vote counts as well).
Once the vote is taken, if AT LEAST 50% of the vote is in your favor
the pirates must abide by your decision of who gets what share. However,
if you do NOT get at least 50% of the vote, the other pirates KILL you,
and then the next oldest pirate gets to decide what shares the remaining
pirates will get. Of course, even the next oldest pirate's plan would
have to be voted on, making it possible that he could be voted out
and killed and it would repeat for 3 pirates then 2, etc.
Assuming all 5 pirates, including you, are equally intelligent and
all have only these goals: 1) Get as much gold as possible for themselves
and 2) Stay alive,
What share would you specify for each pirate, and yourself,
and how would you reason with the pirates to ensure you get
enough of the vote to stay alive and keep your share?