Logic puzzles

This Thursday is Pi Day, the one day of the year devoted to a mathematical constant (it also happens to be Einstein’s birthday). We all learned as kids about how special pi is and have since accepted its cultural status as a geeky totem and a number worth celebrating. But perhaps we should revisit pi through the jaded lens of adulthood. The circumference of a circle is always 3.14… times its diameter. Big whoop! The perimeter of a square is four times its side length, but we don’t assign special significance to the number…

Alicia and Bruno are each given a different natural number in secret (1 is the smallest natural number, 2 is the second smallest, and so on). They are then tasked with guessing which of them has the larger number. The following conversation ensues:Alicia: I don’t know who has the bigger number.Bruno: I don’t know either.Alicia: Upon further reflection, I remain ignorant.Bruno: Alas, I’m still unsure too.Alicia: Now that you say that, I actually know which of us has the bigger number!Bruno: Cool! In that case, I know what…

We all keep secrets. It’s easy to do once you’ve committed to it. Just don’t say anything. But it can be harder when you want to share a little bit of information, without your confidante inferring tea that you didn’t intend to spill. Computer scientists often draw this distinction between security and privacy. Security focuses on keeping sensitive data out of the hands of untrusted parties, full stop. Privacy, on the other hand, aims to give people fine-tuned control over how their personal data gets distributed and…

Every few months, a math problem goes viral on social media. Disappointingly often, it lacks mathematical meat. It seems over half of them boil down to the order of operations. Some tweet will get thousands of likes claiming that the Internet is divided over an arithmetic problem like: what does 6÷2(1+2) equal? It’s fine if people don’t remember how to evaluate expressions like this. But it’s not so interesting when you just have to Google the order of operations and follow the instructions (it equals 9).“Even AI Rappers…

One of the most famous logic puzzles of all time involves a fork in the road, where one path leads to freedom and the other leads to your death. Each path has a guard, and one of them always tells the truth and the other always lies, but you don’t know which is which. You get to ask one yes/no question to one guard to guarantee your road to freedom. What do you ask? It won’t work if you simply ask one of them, “Does your road lead to freedom?” because if they reply, “Yes,” then it could be a truth-teller setting you free…

It’s best to solve this week’s puzzle (really, three mini-puzzles) without an introduction. I’ll explain why after you’ve given it a shot.Alex Borstein’s Embarrassing Moment from Catwoman | io9 InterviewDid you miss last week’s puzzle? Check it out here, and find its solution at the bottom of today’s article. Be careful not to read too far ahead if you’re still working on that puzzle!Puzzle #8: The Cognitive Reflection TestA bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball…

What are the shortest words with a given number of syllables? “I” and “a” each contain one letter and one syllable, which is the tightest ratio we could realistically expect. Are there any two-letter words with two syllables? The only one I’m aware of (not counting things like “BB,” as in “BB gun”) requires that we allow proper nouns: Io, Jupiter’s closest moon (pronounced “eye-oh”). I don’t think we can extend the 1:1 ratio to three letters. Some four-letter words with three syllables include Ohio, Iowa, and iota.…

To most, Lewis Carroll is best known as the whimsical author of Alice’s Adventures in Wonderland, but did you know that he was also an avid puzzler and published mathematician? Among his many contributions was a book of mathematical puzzles that he called “Pillow Problems.” They are so named because Carroll devised them in bed to distract himself from anxious thoughts while falling asleep. He wrote that while stirring in bed, he had two choices: “either to submit to the fruitless self-torture of going through some…

Image: Photo: Shutterstock Graphics: Vicky LetaGames are a bottomless reservoir of puzzle inspiration. This is because games and puzzles both tend to be founded on a concise set of logical rules. This week’s puzzle concerns one of the simplest strategy games ever devised: tic-tac-toe. Don’t feel too assured, though. You may be a tic-tac-toe expert, but have you ever tried to play it backwards?Did you miss last week’s puzzle? Check it out here, and find its solution at the bottom of today’s article. Be careful not to read…

Leer en español.OpenAI’s ChatGPT has apparently invented a new game called Sumplete that has the potential to dethrone Wordle. The artificial intelligence model did receive some human help to develop its game from a human user, Daniel Tait, who guided the chatbot and created a website for the game so anyone can play.Sumplete is similar to Sudoku, although its rules are different. Players are given grids with numbers that vary in difficulty. The basic one for beginners has three rows and three columns, increasing in…