One of the most famous logic puzzles of all time involves a fork in the road, with one path leading to freedom and the other leading to death. Every path has a guardian and one of them always tells the truth and the other always lies, but you don’t know which is which. You can ask a guard a yes/no question to guarantee your path to freedom. what are you asking It won’t work if you simply ask one of them, “Is your path leading to freedom?” Because if they answer “yes,” it could be a fortune teller setting you free or a liar leading you to freedom condemned to death.
This riddle was introduced in 1986 in the LSD trip. labyrinthand the protagonist solved the problem by asking one of them, “Would he other Guard, tell me your way leads to freedom?” The clever combination of the two Guardians ensures that you don’t get bad advice (e.g. if the Guardian says “No”, choose his path, and if the Guardian says “Yes”, choose the other path). The idea behind this is that a lie about the truth or the truth about a lie both provide reliably bad information that you should dismiss. A solution that I like even better is to ask a security guard, “What would you say if I asked you if your path led to freedom?” This subtle rephrasing forces the liar into a double negative. I invite you to work through the details.
Legendary logician Raymond Smullyan dubbed these puzzles “Knights and Villains” and spawned dozens of variations in his writings, including this week’s Monday puzzle. The so-called “The hardest logic puzzle ever“Stars Knights and Villains and requires the solvers to ask three cracking questions. While this riddle is absolutely stunning, I’m tempted to say that the riddle I’m presenting below is the hardest riddle of its kind where you only ask a single question. Let me know in the comments if you have any other candidates.
Did you miss last week’s puzzle? Listen Here, and find the solution at the end of today’s article. Be careful not to read too far ahead if you haven’t completed last week’s tasks!
Mystery #11: Smullyan’s Truth Engines
A magic shop sells divination machines. The machines each have a yellow light and a blue light that illuminate in response to right-or-false questions, with one light corresponding to ‘true’ and the other to ‘false’. The shopkeeper has three machines. She tells you that two of them are working and telling the truth, but one of them is broken and giving out random answers. She doesn’t know which one is broken. In addition, she does not know which light colors correspond to “true” and “false”, and the meaning of the lights may differ from machine to machine (e.g. in one machine a yellow light could mean “true” while in another machine a yellow light could mean “true”). “INCORRECT”). ask a singles right-or-wrong question one machine to ensure you walk away with a working truth machine.
Machines that answer randomly are a lot harder to control than villains who always lie. Consistent liars mislead in predictable ways! It’s even harder not knowing what the lights mean and that they can be different depending on the machine. While not for the faint of heart, this puzzle is for determined mortals may solve it.
Discuss your thoughts in the comments and I’ll get back to you with the solution and a new puzzle next week. Do you know a cool riddle I should cover here? Send it to me at email@example.com
Solution to Puzzle #10: Physics Stumpers
I left you last week two puzzlesread from the physical world. Kudos to spessartine to give good Concise explanations for both puzzles.
The first challenge was:
- You have a scalding cup of coffee that is too hot to drink. You can either pour in a splash of cold milk and let it sit for 10 minutes, or let it sit for 10 minutes first and then add the milk. In what scenario does the coffee end up being cooler, or are they both equivalent? In both cases, assume that you are pouring the same amount of milk and that the milk is at the same temperature.
The coffee will be cooler if you first let it stand for 10 minutes and only then pour in the milk. There are two ways in which the coffee loses heat. One is by releasing it into the environment and the other is by transferring heat to the cold milk until it mixes and reaches a (cooler) temperature. Crucially, the hotter things are, the faster they give off heat to their surroundings. So when the coffee is at its hottest, it loses heat very quickly. Adding milk immediately slows this loss, instead the early heat is transferred to the milk and stays in the mug. For cooler coffee, it is better to leave it standing Give the air as much heat as possible before pouring in milk.
The second question:
- You are in a canoe in the middle of a pond and you brought a rock. You pick up the stone, drop it in the water and watch it sink to the bottom. Does the water level of the pond rise or fall (albeit imperceptibly) or does it stay the same?
The water level drops when you throw the stone into the pond. A submerged object displaces its volume. In other words, imagine the stone was made of water and we poured that water into the pond. That would raise the level of the pond as much as submerging the rock. A floating object, on the other hand, displaces it Weight in water. That is, if the rock is in the canoe and the rock weighs 1 pound, it will contribute one pound worth of water to the height of the pond. So the question arises: what is more – an amount of water equal to the volume of the rock or an amount of water equal to the weight of the rock? Weight wins this competition. In fact, we know this because the stone sinks. Ordinary objects sink in water precisely when it would take more water to balance their weight than to balance their volume. Had the rock been a little much less dense, say a large, airy pumice stone, its volume in water might exceed its weight in water, and such a rock would have floated.
Ice floats in water. As a nice bonus teaser, what happens to the water level in a glass when the ice melts? Does it rise, fall or stay the same? Let me know what you think in the comments.
Last week I posted a bonus poker question in the solution section, courtesy of reader Joshua Lehrer: Imagine playing Texas Hold’em against an opponent, you could choose which two cards you’re dealt and which two cards you’re dealt . Then the dealer turns over the five community cards without having to bet between them (you might be all-in). Which cards should you choose for yourself and your opponent to maximize your chances of winning?
My gut feeling was to pick the best hand for myself (two aces) and the worst hand for my opponent (a non-matching 7 and a 2). Turns out you can do better if you can pick both hands. Salute to the reader donnie from Las Vegas who emailed me the correct answer. The answer is to give yourself two kings and your opponent a king and a 2, where the 2 is a suit with one of your kings. Terribly unexpected! Apparently, this gives the side with the two kings a 94.16% chance of winning, while two aces against the 7 and the 2 give only an 88.74% chance of winning.