In front of you, there are 9 coins. They all look absolutely identical, but one of the coins is fake. However, you know that the fake coin is lighter than the rest, and in front of you is a balance scale. What is the least number of weightings you can use to find the counterfeit coin?
If two fifty-foot ropes are suspended from a forty-foot ceiling that is twenty feet apart, how much rope will you be able to steal if you have a knife?