Searching for a chocolate coin
In a game show, you are given a bag filled with 2,000 coins. 1,999 of them are gold and one is chocolate Chanukah gelt. The coins all look and feel identical, but if you can find the chocolate one, you get to keep all of them.
To help you, the host gives you a measuring scale which can compare two weights (and indicate which side weighs more). You're told that the gold coins each have equal weight, and the chocolate one weighs less. You are allowed to use the scale a certain number of times. Each time, you can put any number of coins on each side of the scale.
What is the least number of times you need to be able to use the scale in order to guarantee a winning strategy for you?
Assume you can't smell the chocolate and that it's hard enough to not get crushed by the other coins.
The answer is 7.
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1 solution
The best way to do this is to separate the pile into 3 piles of equal size (or as close to equal size as can be). Then weigh two of the piles. Since we know the chocolate coin is lighter then you will know with one weighing which pile the chocolate coin is in (if they're equal, then it's in the third unweighed pile. If one is lighter, then it's in that pile). Since we are starting with 2000 coins then you can separate into three piles, and each one into 3 smaller piles, etc, and on the 7th try your piles will be of one so you'll know which is the coin.