The math department here at JMU has a Problem of the Week competition, and it just so happens that, this semester, I am running it. Every week I choose a problem for the consideration of all who choose to participate. (Well, I actually bribe my students to participate by offering them a bonus point for each problem they get right, but whatever.) A randomly selected winner from among the correct answers gets a five dollar gift card to Starbucks. Mostly it’s just a way to get the students thinking about amusing mathematical brainteasers outside of their regular coursework.
Anyway, I am especially fond of this week’s puzzle, even if it does stretch the definition of a math problem just a bit. It makes me smile every time I read it. It’s not terribly difficult, but I think you might enjoy working it out:
The Supreme Court today reversed its earlier ruling that let stand an appellate court’s decision to overturn a lower court’s finding that a restaurant owner had no right to fire a waiter for refusing to deny service to a male patron who was not wearing a tie and jacket. If a male patron now enters the restaurant, and if we assume that the wait staff will serve anyone as long a they are confident they will not be fired for doing so, then will the male patron be served?
There’s practically a whole genre of puzzles along these lines, in which a situation is described in language specifically intended to be confusing. Your task is to decipher what is going on. In the Problem of the Week I provide a second example as a warm-up exercise:
If you ask me on Friday what day classes start, and I truthfully reply that they start two days after the day before the day after tomorrow, then on what day do classes start?
Of course, the granddaddy of this genre is this old chestnut:
A man is looking at a painting of a certain person. You ask him who he is looking at. He points to the person in the painting and replies, “Brothers and sisters I have none, but this man’s father is my father’s son.” Who is shown in the painting?
Actually, this one provides a useful clinic for how to solve such a thing. Usually, the simplest way is to work backward from the end. If I am a man with no siblings, then my father’s son is me. Thus, the statement in the problem amounts to saying, “I am the father of the man in the painting.” So the man is looking at a picture of his son.
As a variant on the previous problem, how would the answer change if the man had said, “Brothers and sisters I have none, but this man’s son is my father’s son.”?
If that was too easy for you, then have a go at a tougher one:
Jill knocks on Jack’s door. When Jack answers, Jill says to him, “Remember that book you lent me? Well, I lent it to my mother, and she lent it to her sister, who gave it to her son-in-law, who thought his wife’s maternal grandfather would like it. He did, and lent it to his wife, who gave it to her son, John. Last night John dropped in and asked me to return it to his son. So here it is.” How are Jack and Jill related?
How about one more before I sign off?
“Hi Bill. Let’s meet at my office, okay? The building is on the North side of Main Street. After entering through the front door, turn left down the hall and take one of the elevators on your right as high it goes. Across the hall there’s another elevator. Take it to the 50th floor. When you get out, turn left and look for a door on the right that says UP. Go in, turn right up a short staircase, then turn left through the exit door at the top of the stairs. Walk down the hall that goes to your right, and my office door is on the left.” Which direction will Bill be facing when he knocks on the door?
Frankly, even if you’re not interested in trying to solve them, I think these puzzles work well just as poetry!