You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, how can you determine which coin is counterfeit using the scale only twice?
First weigh three coins against three others. If the weights are equal, weigh the remaining two against each other. The heavier one is the counterfeit. If one of the groups of three is heavier, weigh two of those coins against each other. If one is heavier, it’s the counterfeit. If they’re equal weight, the third coin is the counterfeit.
A man gets off the bus looking for an address and approaches a couple walking in the same direction for directions. The woman says they’re going that way and take him. Along the way the man asks if they’re related. The woman grins and says, “We’re not strangers. This man’s mother is my mother’s mother-in-law.” The man is confused but doesn’t say anything. When he gets back home he tells his wife about the conversation and she can’t figure it out either. They decide to ask their lawyer and he eventually works it out with pen and paper. How are the couple related?