Occasional Puzzles - Tipping the scales
Today’s Puzzle
You have ten bags of coins, each containing 1000 coins. One of the bags, though, is full of counterfeit coins - instead of weighing 1 gram each, they weigh 1.1 grams each. You have a digital scale, but you can only use it once. How do you identify which bag contains the counterfeit coins?
Last Saturday’s Puzzle - Three logicians walk into a bar…
Three logicians walk into a bar. The bartender asks, “Do all three of you want a drink?”
The first logician says, “I don’t know.”
The second logician says, “I don’t know.”
What does the third logician say?
[SPOILER] Answer to Last Saturday’s Puzzle
The third logician says “yes” if she wants a drink and “no” if she doesn’t.
The bartender asks if all three of them want a drink. If the first logician doesn’t want a drink, he’ll say “no”, since that would mean not all of them wanted a drink. Instead, by saying “I don’t know”, he indicates that he does want a drink, but doesn’t know about the other two. The second logician follows the same reasoning. Thus the third logician knows that both of the first two want a drink. So, if she wants a drink, then all three of them want a drink and she’ll say “yes”. If she doesn’t want a drink, then not all three of them want a drink, and she’ll say “no”.