Channel: singingbanana

Category: Education

Tags: james grimeproblemsquare root of 2mathspuzzleirrational numbersmathlogicalex bellosdeductive reasoning

Description: Jack is looking Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person? A) Yes B) No C) Cannot be determined Here is the solution and results from the survey on Alex Bellos' Puzzle blog: theguardian.com/science/2016/mar/28/did-you-solve-it-the-logic-question-almost-everyone-gets-wrong A short video of my reaction to the survey youtu.be/-iSxls2f0Qo And check out more puzzles from Alex Bellos here: theguardian.com/science/series/alex-bellos-monday-puzzle ----- Some interesting variations have been suggested. These include: 1. A coin is flipped three times. The first is a head. The third is a tail. Is a head ever followed directly by a tail? This is the same problem but it seems easier to solve. 2. Jack is sat next to Anne. Anne is sat next to George. Jack is married, George is not. Is a married person sat next to an unmarried person? This makes the relations bidirectional and seems easier to solve. 3. We can also extend the married problem to as many people as we like. If M is married, and U is unmarried, then M sees ? sees ? sees ? sees .... sees ? sees U. Is a married person looking at an unmarried person? Well, at some point there is a transition from Married to Unmarried and so the answer is yes. 4. The dictionary definition of unmarried is "not married". This includes everything that is not married, i.e. widowed, divorced and single. Whatever you definition of marriage this makes married and unmarried a binary choice. However, here is another suggestion using "alive" and "dead" "I found a picture from 50 years ago of my grandmother and grandfather on a ski trip together. In the picture, my grandfather is looking at the ski instructor, and the ski instructor is looking at my grandmother. My grandfather is still alive but my grandmother died last year. Is someone in the picture who is still alive looking at someone who is now dead?" (waits for people to argue the ski instructor might be a zombie) ---- Here are some other observations I want to add after seeing some questions in the comments: 1. You can construct an explicit example to whether an irrational number to an irrational power can be rational if we know transcendental numbers exist. (That means it's not a solution to a polynomial with rational coefficients). Then we can take x transcendental and x^log_x(2) = 2. x is irrational, and log_x(2) is irrational, otherwise we have x^(p/q) = 2 and so x^p = 2^q contradicting the transcendentality of x. So e^ln(2) = 2 would do it. 2. Can a rational number to an irrational power be rational? Indeed, for example 10^log(2) = 2. It is easy to show log(2) is irrational, otherwise we would have 10^(p/q) = 2 and so 10^p = 2^q which violates unique prime factorisation. ---- A final word to those who argue that Anne might not be a person (a dog etc). If that had been the answer then the question would have been a riddle rather than a logic problem. A riddle invite you to guess information not presented in the question, or hidden in the question. A logic problem asks you to make deductions from the information presented in the question only, and specifically not using information from outside the question. It is always possible to circumvent logic problems with left-field answers, but that isn't really in the spirit of the question and would miss the point of the exercise. So it's important to know that you are answering a logic problem, and how they work, before you start. Since Alex and I run maths blogs we will only present logic problems and never riddles. ----- If you have read the description you are part of an exclusive club. Welcome. Your challenge is to work a Steven Spielberg movie title into a comment below.