http://io9.com/can-you-guess-the-next-number-in-this-sequence-1659351437rtgonzalez@io9.com1 11 21 1211 111221 312211 ?Robbie GonzalezFiled to: SUNDAY PUZZLEMATHEMATICSMATHS11/16/14 11:00amEverything you need to solve this riddle can be found in the numbers you see here. Be apprised: The mathematically inclined tend to struggle with this puzzle.I'm on the road this week, so this week's puzzle is short and sweet but still quite challenging, in my opinion. It's another classic, so if you know the answer try not to spoil it in the comments.We'll be back next week with the solution and a new puzzle! Got a great brainteaser, original or otherwise, that you'd like to see featured? E-mail me with your recommendations. (Be sure to include "Sunday Puzzle" in the subject line.)"This scenario is somewhat similar to a famous Indian riddle, which is at least 1,000 years old, since it occurs at the climax of the Baital Pachisi," writes Phil Winkelman,who originally suggested this puzzle via our Sunday Puzzle tips line. "However, in this tale, a man and his son meet a woman and her daughter the man marries the daughter and the woman the son. This scenario reached its cultural apogee (or nadir) in 'I'm My Own Grandpa'." (Some of you noted the similarities between this puzzle and "I'm My Own Grandpa" in the comments.)http://en.wikipedia.org/wiki/Baital_PachisiTwo old men [M1, M2] each of whom has a grown-up son [M3, M4] each of whom has an unmarried daughter [F1, F2] marry two young girls who are sisters [F3, F4]. After the wedding, however, the two old men are ill and die before the marriages are consummated. After their deaths the two young men marry their stepmothers: these six last [shaded boxes] are those who lie buried here. For here two sisters are also lying with their two brothers[-in-law], because every woman calls her sister's husband her brother."Not only is there a fudge-factor with the stipulated 'brothers' actually panning out as brothers-in-law," writes Winkelman, but Lichtenberg's preliminary solution requires that daughters, mothers, and grandmothers be regarded as step-relations. "The correct solution," he notes, and as we see in Edward's solution above, "does not require these feints."http://io9.com/youll-want-to-give-up-on-this-weeks-puzzle-dont-1662370735Solving This Puzzle Will Help You Grasp the True Nature of PuzzlesRobbie GonzalezRobbie GonzalezFiled to: SUNDAY PUZZLESCIENTIFIC PROBLEM SOLVINGG. POLYA11/23/14 12:45pmYou'll want to give up on this week's puzzle. Don't.The key to unraveling this week's puzzle is the key to cracking most good brain teasers: If you want to solve it, you're going to have to get organized.Before We Begin...I'm going to come right out and say it: Our puzzle this week involves math. I see some of you clicking away already. To you I say: Don't be intimidated. Yes, you will need algebra to solve this puzzle, but the most difficult aspect of this week's brain teaser, in my opinion, doesn't boil down to math. It boils down to organization.A few weeks ago, somebody asked in the comments if a math problem could really be considered a "puzzle." (I can't find the comment now, but I think it was made in reference to the posted solution for The Logician's Children.) The answer to this question is, of course, yes. Martin Gardner, one of the most prolific puzzle-posers of the 20th century, built his career, in large part, on mathematical puzzles. A lot can be said about why math problems make for excellent puzzles, but the simplest explanation I can provide is that a good math problem demands to be solved by means of a carefully organized approach.Entire books could be written about this last point. In fact, they have been: How to Solve It, the classic text by mathematician G. Plya, is considered by many to be the definitive guide to mathematical problem solving. In his book, Plya outlined a list of best practices for confronting puzzles of the mathematical variety. His approach, originally written in 1945, has since been distilled into a plan of attack by Herman Gordon, associate professor of cell biology and anatomy at the University of Arizona, and instructor of The Art of Scientific Discovery, a course designed to hone students' skills at solving the kinds of problems one encounters in medicine and scientific research. Gordon's guide walks us through the way a good mathematician (and a good problem solver) thinks. "Even though the topic is logic," he writes, "the discovery and solution of mathematical problems involves induction and heuristic thinking:1. Understand the problemWhat is the unknown?What are the data?What is the condition?Can the problem be solved?2. AssumptionsWhat can you or need you assume?What shouldn't you assume?Have you made subconscious assumptions?3. Devising a plan of attackHave you seen this or a related problem before?Have you seen a similar unknown before?Can you restate the problem?If you can't solve this problem, can you solve a similar or simpler problem?4. AftermathAre you sure of the solution? Can you see it at a glance?Did you use all the data? The whole condition?Can you get the same solution another way?Are there other valid solutions?Can you apply the solution or method to another problem?Was this a satisfying problem to solve?If you ever find yourself struggling with a Sunday Puzzle, or any puzzle for that matter, look to these guidelines. Print them out. Stick them above your desk. I guarantee you will find this guide or, at the very least, some part of it helpful when puzzling your way through a good brain teaser, be it a math problem, a logic puzzle from our weekly column, or a line of scientific inquiry.Becoming a better problem solver requires practice. You need to be organized. And you need to think about your thinking. With all that in mind, here is this week's puzzle.Sunday Puzzle #8: A Monkey And His UncleA monkey and his uncle are suspended at equal distances from the floor at opposite ends of a rope which passes through a pulley. The rope weighs four ounces per foot. The weight of the monkey in pounds equals the age of the monkey's uncle in years. The age of the uncle plus that of the monkey equals four years. The uncle is twice as old as the monkey was when the uncle was half as old as the monkey will be when the monkey is three times as old as the uncle was when the uncle was three times as old as the monkey. The weight of the rope plus the weight of the monkey's uncle is one-half again as much as the difference between the weight of the monkey and that of the uncle plus the weight of the monkey.How long is the rope?How old is the monkey?This week's puzzle was submitted by Reid (a mathematician) in retribution, he says, for last week's puzzle, which despite appearances actually required no mathematical skills whatsoever to solve.We'll be back next week with the solution and a new puzzle! Got a great brainteaser, original or otherwise, that you'd like to see featured? E-mail me with your recommendations. (Be sure to include "Sunday Puzzle" in the subject line.)Art by Jim Cooke@#http://io9.com/can-you-solve-the-hardest-logic-puzzle-in-the-world-1642492269Can You Solve 'The Hardest Logic Puzzle In The World'?619,826105rtgonzalezRobbie GonzalezProfileFollowRobbie GonzalezFiled to: SUNDAY PUZZLEPUZZLESWEEKLY PUZZLEPUZZLING100 GREEN EYED DRAGONS10/05/14 10:30amYou're reading the first installment in a brand new puzzle series here at io9 and what better way to kick things off than with the world's most difficult logic puzzle?The Sunday Puzzle - An IntroductionSome months back, I posted a little brain teaser here on io9. People seemed to enjoy it. Encouraged by the positive response, I decided to float an idea I'd had bouncing around my head for some time: How would you all feel about me dedicating one post per week to a particularly dastardly puzzle or brain teaser?, I asked. Again, lots of positive response. The idea for The Sunday Puzzle was born. Can You Figure Out This Parking Lot's Numbering System?Can you explain the numbering system in this parking lot? Like most good riddles, there are several Read moreI confess this idea was not entirely my own. The genre of public, published puzzling was arguably pioneered by the legendary Martin Gardiner and his 'Mathematical Games' column in Scientific American, and lots of places to this day post puzzles and riddles with some regularity. But the clearest inspiration for io9's Sunday Puzzle was the TierneyLab blog over at the New York Times, where John Tierney used to publish puzzles, and discussions surrounding previous weeks' puzzles, every Monday.I'd like io9's Sunday Puzzles to follow a similar format to Tierney's, and for the comments to become a place for people to submit full or partial solutions, questions, ideas, future puzzles, and so on. I encourage you to also upload any drawings, calculations, or ideas you jot down in the course of your puzzling. I'm still sorting out the details (I like to think that our commenting system has the potential to be moderated in a way that will foster discussion and help people along in the puzzle-solving process, without always spoiling the solution outright but how feasible this will be in practice remains to be seen), so recommendations on how to structure the column are of course welcomed and encouraged.There's so much more I could say about this, but I'll refrain for now (or reserve it for future posts), save for one last thing: If you know a great brain teaser that you think would work well as a Sunday Puzzle, please feel free to drop me a line with "Sunday Puzzle" in the subject line. Or sound off in the comments. Please also indicate whether it is an original puzzle or one that you found elsewhere. Puzzles can be mathematical, logical, visual, computational, some combination thereof, etc. but they should be challenging, and, of course, satisfying to solve. (More on what constitutes a satisfying puzzle in future posts.)Alright. I'm going to stop talking now (can you tell I'm really excited about this?). Onto the puzzles.Sunday Puzzle #1: 100 Green-Eyed DragonsUPDATE: SOLUTIONThis week's puzzle is an old favorite of mine. It's been around for a long time, and existed in various forms, but the version we'll be solving I originally encountered in a handout given to physics students at Harvard, and is called "Green Eyed Dragons."XKCD's Randall Munroe tells a version of this puzzle, called "Blue Eyes," that he's dubbed "The Hardest Logic Puzzle In The World." The puzzle is fundamentally identical to Green-Eyed Dragons, but Munroe's version includes some wording that provides what I think is a fairly big clue, so if you find yourself struggling with the dragons, head on over to XKCD and give his rendition a go. Here, now, is what I believe to be the most challenging version of the puzzle:You visit a remote desert island inhabited by one hundred very friendly dragons, all of whom have green eyes. They haven't seen a human for many centuries and are very excited about your visit. They show you around their island and tell you all about their dragon way of life (dragons can talk, of course).They seem to be quite normal, as far as dragons go, but then you find out something rather odd. They have a rule on the island which states that if a dragon ever finds out that he/she has green eyes, then at precisely midnight on the day of this discovery, he/she must relinquish all dragon powers and transform into a long-tailed sparrow. However, there are no mirrors on the island, and they never talk about eye color, so the dragons have been living in blissful ignorance throughout the ages.Upon your departure, all the dragons get together to see you off, and in a tearful farewell you thank them for being such hospitable dragons. Then you decide to tell them something that they all already know (for each can see the colors of the eyes of the other dragons). You tell them all that at least one of them has green eyes. Then you leave, not thinking of the consequences (if any). Assuming that the dragons are (of course) infallibly logical, what happens?If something interesting does happen, what exactly is the new information that you gave the dragons?I will make the same closing points here that Munroe does: This is not a trick question. There's no guessing or lying or discussion by or between dragons. The answer does not involve Mendelian genetics, or sign language. The answer is logical, and the dragons are perfectly logical beings. And no, the answer is not "no dragon transforms."We'll be back next week with a breakdown of the solution and a new puzzle!Illustration by Jim Cooke@# http://io9.com/to-solve-this-riddle-look-to-your-family-1654578754This week's puzzle is about a perplexing pedigree. Can you untangle its twisted lines of descent?Sunday Puzzle #6: The Riddle Of The Six-Grave Plot (aka "Lichtenberg's" Riddle)While ambling about your local cemetery, you stumble upon a grave marker situated before a six-grave plot. Glancing down, you notice an inscription upon the family stone. It reads:Here lie...2 Grandmothers with their 2 Granddaughters2 Husbands with their 2 Wives2 Fathers with their 2 Daughters2 Mothers with their 2 Sons2 Maidens with their 2 Mothers2 Sisters with their 2 Brothers...Yet but 6 corpses all lie buried here,All born legitimate, from incest clear.How is this possible?@#http://io9.com/either-you-solve-this-riddle-or-you-die-1653822870Answer this week's riddle incorrectly, and your life and the lives of 22 others will be forfeit.Sunday Puzzle #5: 23 Prisoners, 2 SwitchesA warden meets with 23 newly arrived prisoners. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another."In the prison is a switch room, which contains two light switches, each of which can be in either the on or the off position. I am not telling you their present positions. The switches are not connected to anything."After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must move one, but only one of the switches. He can't move both, but he can't move none, either. Then he'll be led back to his cell."No one else will enter the switch room until I lead the next prisoner there, and he'll be instructed to do the same thing. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back."But, given enough time, everyone will eventually visit the switch room as many times as everyone else. At any time anyone of you may declare to me, 'We have all visited the switch room.'"If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will all be executed."What strategy do the prisoners devise?This is another classic puzzle, but one worth revisiting even if you've heard it before. (If you have heard it, and remember the solution, I suggest checking out this version). Five or six of you recommended this puzzle, or a variation of it, this week, so thanks to all of you who did but thanks to David, in particular, for being the first to do so. We'll be back next week with the solution and a new puzzle! Got a great brainteaser, original or otherwise, that you'd like to see featured? E-mail me with your recommendations. (Be sure to include "Sunday Puzzle" in the subject line.)Art by Jim Cooke@#http://io9.com/youll-need-all-3-clues-to-solve-this-puzzle-1650957105We're back this week with another logic puzzle. For this one, you'll need all the help you can get.Sunday Puzzle #4: The Logician's ChildrenTwo former college roommates, both logicians, meet at a conference after many years without contact. While catching up, the two eventually get around to discussing their children. The first logician asks the second how many children he has, and what their ages are. The second replies that he has 3 children, but (ever the logician) he will only reveal clues about their ages. The first logician must deduce for himself the ages of the second's children."First," says the logician, "the product of my children's ages is 36.""Second, the sum of their ages is the same as our apartment number in college.""Third, my oldest child has red hair."Upon hearing the third clue, the first logician replies at once with the ages of his friend's children. What are they? How do you know?Many thanks to BJ Myers for suggesting this week's puzzle. We'll be back next week with the solution and a new puzzle! Got a great brainteaser, original or otherwise, that you'd like to see featured? E-mail me with your recommendations. (Be sure to include "Sunday Puzzle" in the subject line.)http://en.wikipedia.org/wiki/Baital_PachisiVetala Panchavimshati (Sanskrit: ???????????????, IAST: vetalapacavi?sati or Baital Pachisi (Bengali) ("Twenty-five (tales) of Baital"), is a collection of tales and legends within a frame story, from India. It was originally written in Sanskrit.One of its oldest recensions is found in the 12th Book of the Kathasaritsagara ("Ocean of the Streams of Story"), a work in Sanskrit compiled in the 11th century by Somadeva, but based on yet older materials, now lost. This recension comprises in fact twenty four tales, the frame narrative itself being the twenty fifth. The two other major recensions in Sanskrit are those by Sivadasa and Jambhaladatta.The Vetala stories have been popular in India, and have been translated into many Indian vernaculars.[1] Several English translations exist, based on Sanskrit recensions and on Hindi, Tamil, and Marathi versions.[2] Probably the most well-known English version is that of Sir Richard Francis Burton which is, however, not a translation but a very free adaptation.[3]The legendary King Vikrama, identified as Vikramaditya (c. 1st century BC), promises a vamachari (a tantric sorcerer) that he will capture a vetala (or Baital), a celestial spirit analogous to a vampire in Western literature who hangs from a tree and inhabits and animates dead bodies.King Vikrama faces many difficulties in bringing the vetala to the tantric. Each time Vikram tries to capture the vetala, it tells a story that ends with a riddle. If Vikrama cannot answer the question correctly, the vampire consents to remain in captivity. If the king knows the answer but still keeps quiet, then his head shall burst into thousand pieces. And if King Vikrama answers the question correctly, the vampire would escape and return to his tree. He knows the answer to every question; therefore the cycle of catching and releasing the vampire continues twenty-four times.On the twenty-fifth attempt, the Vetala tells the story of a father and a son in the after-math of a devastating war. They find the queen and the princess alive in the chaos, and decide to take them home. In due time, the son marries the queen and the father marries the princess. Eventually, the son and the queen have a son, and the father and the princess have a daughter. The vetala asks what the relation between the two newborn children is. The question stumps Vikrama. Satisfied, the vetala allows himself to be taken to the tantric.http://i.kinja-img.com/gawker-media/image/upload/s--6kkihzg2--/xj0dumyt78cc1gcvkm89.jpg@#http://io9.com/the-whys-wherefores-and-wonders-of-mathematics-1698504193http://www.youtube.com/embed/V1gT2f3Fe44Log in / Sign upFollowRELATED BLOGSObservation DeckSpaceAnimalsToyboxTrue CrimeBLOGS YOU MAY LIKEDeadspinGawkerGizmodoio9JalopnikJezebelKotakuLifehackerSploidundefinedYour profileCompose postAccount SettingsView DashboardLogoutMY BLOGSTRENDING ON KINJA1.That Awkward Moment When Hideo Kojima Doesn't AppearThat Awkward Moment When Hideo Kojima Doesn't Appearon Kotaku2.Tesla's New Battery Could Solve One of Solar Power's Biggest Problemson Gizmodo3.What Game Designers Love (And Dont Love) About Souls Gameson KotakuWRITTEN BY ROBBIE GONZALEZWhy Are There Clouds And How Do They Form?Why Are There Clouds And How Do They Form?Everything You Need to Know to Catch This Week's Lyrid Meteor ShowerEverything You Need to Know to Catch This Week's Lyrid Meteor ShowerLarge-Scale Study Confirms: Still No Link Between MMR Vaccine and AutismLarge-Scale Study Confirms: Still No Link Between MMR Vaccine and AutismThe Whys, Wherefores, and Wonders of Mathematics6,9016rtgonzalezRobbie GonzalezProfileFollowRobbie GonzalezFiled to: MATHSPAUL LOCKHARTMATHEMATICSSCIARTSCIENCE4/17/15 3:40pmShare to KinjaShare to FacebookShare to PinterestShare to TwitterGo to permalinkCheck out this delightful video of math teacher Paul Lockhartauthor of Measurement, "a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living"waxing lyrical about the splendors of mathematics and mathematical thinking, and why "the mathematical question is always 'why?'"H/t Aatish BhatiaContact the author at rtgonzalez@io9.com.6 13Reply All repliesThe following replies are approved. To see additional replies that are pending approval, click Show Pending. Warning: These may contain graphic material.Show pendingsynthozoicsynthozoicProfileFollowsynthozoicRobbie Gonzalez4/17/15 5:30pmFollow synthozoicFlagShare to FacebookShare to PinterestShare to TwitterGo to permalinkIm not a mathematician (Although in a parallel universe, I wish I was.) but I get what this guy is talking about.Time and again, mathematicians discover relations or facts in the realm of mathematics that just blow us away in terms of their perfect, elegant connection of things that might otherwise seem random jumbles. In Eulers identity e is an irrational number, pi an irrational number but, you connect it in the right way with the imaginary unit number, suddenly order emerges again. Cantors proof that a line segment contains exactly the same number of points as an infinite line is another one. Lockharts parallelogram thing is still another. And on and on it goes. Is math created or discovered? Who knows? But it is very surprisingone is tempted to say shockingsometimes.7Replywill-holzWill HolzProfileFollowWill Holzsynthozoic4/17/15 5:51pmFollow will-holzFlagShare to FacebookShare to PinterestShare to TwitterGo to permalinkWell said!Theyre fascinating because they let us see how two different mathematical abstractions converge. :)ReplysynthozoicsynthozoicProfileFollowsynthozoicWill Holz4/17/15 6:02pmFollow synthozoicFlagShare to FacebookShare to PinterestShare to TwitterGo to permalinkLockhart jokingly says its almost like a conspiracy. At least I think he jokingly says it because to really believe that it is a conspiracy puts aside rigor and takes us into the realm of religion or numerology. Some could jokingly say that mathematics is about as close to religion as science gets. And if thats true, things get Lovecraftian very quickly. Because if math reveals the minds of the gods, those are very a l i e n minds indeed! Madness then follows. Replywill-holzWill HolzProfileFollowWill Holzsynthozoic4/17/15 6:15pmFollow will-holzFlagShare to FacebookShare to PinterestShare to TwitterGo to permalinkI generally think of it in degrees of how good is the person/process were dealing with at not accidentally overdefining something or applying a specific conclusion to too wide a set of scenarios, because thats pretty much where the axis between genius and madness lies, right?And when you look at that way, its pretty easy to see whats going on. We do our analysis through a very person-centric lens and while I think the scientific community has been EXCELLENT at offsetting that, any situation where we see something surprisingly symmetrical (Its almost always a pattern or a symmetry, isnt it? Our brains are just primed for that shit!) blows our minds.The reality is that were just bubbling up a really simple mathematical truth and we shouldve gotten it a long time ago but we missed it because of our personal view of things. Thats also probably why there are so many people who are Whoa! and a few who are Duh and a lot of us that go from Whoa! to Whoa, and duh! pretty enthusiastically.Kind of like Vi Harts pi is not special rant (and shes totally right, I have to agree with her as annoying as it is to past-me), right?2ReplysynthozoicsynthozoicProfileFollowsynthozoicWill Holz4/17/15 6:25pmFollow synthozoicFlagShare to FacebookShare to PinterestShare to TwitterGo to permalinkAnd Hart gets right to the nub of Sols argument in the movie Pi. You pick a number as special and you see that number everywhere, ignoring all the cultural baggage that might be skewing things. 2Replywill-holzWill HolzProfileFollowWill HolzRobbie Gonzalez4/17/15 3:56pmFollow will-holzFlagShare to FacebookShare to PinterestShare to TwitterGo to permalinkI love this guy! Hes adorable.Also: I think I see the answer!Oh! Duh!(You guys didnt see all the stuff I just erased. There was lots of it, and it turns out its totally unnecessary.)Its because he chose the midpoints.The moment he selected the midpoints, he established two planes of symmetry in the lines connecting those points. That gives you a parallelogram of some sort.Maybe a better way to say it is If you want to draw a parallelogram inside any 4-sided shape, pick the midpoints.(Math is cool!)1ReplytychodinTychoProfileFollowTychoWill Holz4/17/15 4:04pmFollow tychodinFlagShare to FacebookShare to PinterestShare to TwitterGo to permalinkthe solution to his question is evident if you break it apart into two triangles that share a side. for any triangle you can draw, the vector connecting the midpoints of two sides will always been parallel to the third side. i mean, thats almost obvious because youre just halving the x and y components (and so just halving the magnitude) of the third side to get the midpoint vector anyway. and since a vector is always parallel to itself, and since the two triangles share a side, the vectors connecting their midpoints will also be parallel. thats it. thats the whole conspiracy.2Replywill-holzWill HolzProfileFollowWill HolzTycho4/17/15 4:08pmFollow will-holzFlagShare to FacebookShare to PinterestShare to TwitterGo to permalinkYup, thats exactly what I had in my head with completely different words (and sequence!)I love that, I bet its also possible to solve it by hitting it from the outside somehow.(Math continues to be cool!) 1Replytwilightsparkle2013Twilight SparkleProfileFollowTwilight SparkleRobbie Gonzalez4/18/15 12:10amFollow twilightsparkle2013FlagShare to FacebookShare to PinterestShare to TwitterGo to permalinkThat parallelogram thing doesnt seem scary to me, it seems like something someone wouldnt believe if they had NEVER seen a square or diamond before, even one with vastly smaller sides, of course the middle lines will go in the same direction... DUH.ReplymrifkmrifProfileFollowmrifRobbie Gonzalez4/17/15 4:13pmFollow mrifkFlagShare to FacebookShare to PinterestShare to TwitterGo to permalinkPaul was the best high school math teacher I had. The course was called what is math? And he taught us how to play go, why we may be living in our own flatland, and how most math classs are the equivelant of paint by numbers. A brilliant guy.1ReplyAboutHelpTerms of UsePrivacyAdvertisingPermissionsContent GuidelinesRSSJobsPowered byKINJA