Once you specify a date you get a subset of instances of the original 1/3. Aug. 6, 2012. The game is played on single-screen boards mostly filled with ghosts. Please let me know if this okay with you. It was not PREDICTIVE in nature, but after the fact. You might argue that since we have just replacedBoy with Head, it is the same puzzle and so the chance of the 'other' coin being a Head is 1 in 3. If it isa Head I then say"Ihave two coins, at least one is a Head". This information is filtered and carefully moderated, but incorrect information will inevitably find its way into the system. Home; Museum. When Pac-Man and Rubik's Cube Were Popular Bruce Haight takes us back. unless he wanted to make his margin and saw with Foshee how to make the more money he could). Aside from my trivial adjustments, a dice is a dice. Whats the chance that a second coin flip will be different than the first? Lets boil out all the extra info though, and look at what the problem is really asking. Robert, that is the complete statement of the problem. If I see a tail first I say"At least one is a Tail". (LogOut/ Does Tulsi Gabbard Have A Natural Born Citizen Problem? In fact, if you repeat the question but specify a trait rarer than 1/7 (the chance of being born on a Tuesday), the closer the probability will approach 1/2. As with most probability exercises there is an assumption of all else being constant. The two disciplines are happy bedfellows: both exhibit a wonder at the structure of the world, and seek playful ways to subvert it. Let's call these situations: "There are two Xs, at least one is a Y." Gary Foshee created a popular probability puzzle that goes like this: "I have two children. A well-known probability riddle is I have two children. The 7+7+7+6 formulation is wrong, because the first three situations resulting in 7 outcomes each treat the two births as an ordered pair, while in the last situation the ordered pair is conceptually maintained but the BB pair is discarded because a BB pair appeared in the third situation as well. The question states that one child is a boy. Even if he rounded the end of the rod, its still absolutely usable to unscrew and solve the puzzle.Mine must not have been rounded enough I assume?. Are the odds that the other game will be won by the team that wins the coin toss less than 50-50? Rob M One out of these three scenarios is BB, so the probability of the two boys is 1/3. It consisted of the following three sentences: I have two children. Since you know I have at least one boy, there are three possible pairs of children I might have (older then younger): Each pairing is equally likely, and in only one of these three cases is the'other' child also aboy. High Score. The first thing to remember about probability questions is that everyone finds them mind-bending, even mathematicians. BG and GB are invariant (thats the word I think I was looking for) in this problem statement unless and until you specify the boy was born first or second. If the odds really are 1 in 3, then we should find that the two coins are the same roughly 33 times. . I have two children. In 1 family both children are boys born on a Tuesday Pac Xon is a Pac-Man-inspired title released back in 2007 using Flash, and has since become available . Joshua Frankel 9-Ball Puzzle. If it helps, it could also be stated as at least one is a boy. Either way, this only eliminates one case: GG. So, 14/28. If fair, despite that 6 6s in a row may have come up, the odds of another 6 on the next roll is 1/6th. The remaining cases are BB, BG, and GB, all still of equal probability. I've always claimed that I wasn't much good at it, but many of my friends seem to disagree, so I'm starting to listen to them and do something about it. And only 1/3 of them include a second boy. But 1/3 is not the only valid answer. Dont believe me? One is a boy born in the first half of the day. 154 Georgina Goodlander, coordinator for the Art of Video Games exhibition at the Smithsonian American Art Museum, played. Do we think that Monty Hall was specially chosen because he happened to have two children one a boy born on Tuesday, or was Monty Hall always going to be the speaker and is just describing his particular circumstances. Roy Forsythe Birds of a Feather. Unsurprisingly many who heard it were cross that the answer given in the next episode was 1/3. 52 comments. Why? Gary Foshee, a collector and designer of puzzles from Issaquah near Seattle walked to the lectern to present his talk. Galeries Des MontsSt-Sauveur, PQCanadaJ0R 1R0#Puzzle #Packman #ChrisRamsay Description. But thats not what was stated. What is the probability I have two boys? Note to JJ: Second to last sentence should read 13/27 not 12/27. In typical Foshee syyle, this is a well-made an diabolical puzzle. A witness to a hit-and-run accident tells the police that the license plate of the car in the accident, which contains three letters followed by three digits, starts with the letters AS and contains both the digits 1 and 2. So, consider this preliminary question: I have two children. Grumpy Old Man Archive. Tomid 9.1k members in the mechanicalpuzzles community. The bottom line here is you can only get to a 1/3 answer by assuming that the births are sometimes independent events and at other times dependent events. Hi Neil, great meeting you at IPP35. For example as in the above problem. Magic was chosen as a theme because Gardner himself was an amateur magician and his first foray into mathematics writing in the 1950s was a book on the mathematics of magic. The game is available to play directly within the Google search results page, and features the familiar Pac-Man character navigating through a maze while collecting dots and avoiding ghosts. Actually, the only thing to be learned from this is that poor problem statements can lead to ambiguous results. Conways Life is an example of what is known as a cellular automaton, a grid in which the cells can be either alive (white) or dead (black) and where four simple rules determine what happens to the cells in successive generations. After all, there are only two sexes and its 50/50 the second will be a boy. Mathematicians are especially fascinated by sets of tiles that can only produce a pattern that never repeats. From there on, we can use the same mathematical proof that gave us 13/27 (since regardless of which of the seven days it is, the fraction1/7 for each day still applies). To answer the question you need to first look at all the equally likely combinations of two children it is possible to have: BG, GB, BB or GG. What is the probability I have two boys?. The event was the Gathering for Gardner earlier this year, a convention held every two years in Atlanta, Georgia, uniting mathematicians, magicians and puzzle enthusiasts. How many do you expect to? That is, potentially what are the probabilities of what could have happened? With a little polish Im sure the frame could be cleaned up, so its really a small nit, but given the price of the lock, you do expect a certain level of finish. During the Puzze Exchange, I asked Gary and he directed me to Wil alsoglad I managed to get my hands on an Open Lock. The essential info is that one child is known to be a boy. If someone selected a group of 100 parents who have 2 and only 2 children of whom at least one is a boy, would you be happy to say that 66% of those parents had a girl as the second child? In your example you are only excluding from original set (4) of instances Ba,Ba(1) while excluding from bg,gb set(8) Ba,Gm + Ba,Ga + Gm,Ba +Ga,Ba (4). 9.3K subscribers in the mechanicalpuzzles community. (a - b) (a2 + ab + b^2) I have two children. The Jigazo which will be released in Europe and the US later this year was a product of this traffic. Of course there are things that youll find useful, and the puzzle has much more hidden around it than youd think at first. In 1970 Gardner wrote one of his most widely read columns, on a Conway invention called the Game of Life. Of the three main professions represented mathematicians, magicians and puzzle people the magicians were the easiest to spot: they tended to wear black jackets. Q4) What if, instead of naming a type, I reach in, and pull a out a coin in my closed fist. So BB, BG, GB, and GG are all equally probably, at 25%. This puzzle has always irked me. Better yet, buy one of his books for your kid. Seems like nonsense to me, too. Play over 320 million tracks for free on SoundCloud. Heh. After looking at the first problem in a corrected light, it would turn his notion on its head, but again, this has the same flawed assumption. At least one is a Head. By the way, I really dislike the 7+7+7+6 formulation as well, although it does work out to the correct answer. Seems to me it was a cheesy, gotcha, trick question, and just numerical masturbation after that. 3. . You are incorrect about Marilyn Vos Savant agreeing with you. Rubik's Cube; V-Cube; Meffert's Rotational Puzzles; 2x2; 3x3; 4x4; 5x5; Other Rotational Puzzles; Jigsaws. What is the chance they have two boys. What is the probability I have two boys? I get 3/7 Is this analogous to Charles Austins NFL games and coin tosses? Given how solid it is, its easily a puzzle that you can pass round and let people play with, and theres really not much they can do wrong. In the upcoming reality TV show we scream and bitch slap each other. For more assurance you wouldnt look at BG, GB, or even BTu. Shouldnt the probability change to 1/3 in this case, also? The first thing you think is 'What has Tuesday got to do with it?' Well, it has everything to do with it. One is a boy born on a Tuesday. Or if you choose to consider BG and GB the same case, they were originally 50% possible while BB was only 25% possible, so again, BB is only 25/(50+25) = 1/3 possible. What is the probability I have two boys?. Strange. I will ship it fast during 2-3 days . By this logic, the odds would be 1/3 that if you had two kids, and one was a boy, that both would be boys. Since there are 14 descriptions, and 196 questions, you should expect 196/14=14 questions about each description. Ive been coming back to the original conclusion that Tuesday doesnt matter. Pac-Man, now with ghosts. One last analogy before bed. The puzzle comes in a fairly plain gold box, and as you can see, mine is the 2015 version of the puzzle. You have four possibilities but only three instances\events. An action packed math game which can also be considered as a pac man game with a twist. Franklin et al He was also partly inspired by. Unfortunately Google has removed the Friend Connect service to all non 'Blogger' users so for now I have no way to show followers. I have randomly chosen a parent who has a boy born on Tuesday and just one other child. I would still classify this as a math problem; we used to call these story problems when I was a lad. The principle behind this answer was first published in 1889 by a French Mathematician named Joseph Bertrand, and it is known as Bertrands Box Paradox. The result is the largest assemblage of its kind in the world, with over 30,000 puzzles and 4,000 puzzle related books. The Tuesday/Tuesday scenario should be double counted each boy could be be born on either this or that Tuesday (ie a bit like there are two ways of getting heads and tails with 2 coins) therefore probablitiy is 14/28 + 50%. I was reading her column in Parade at the time. Of course, 12/27 is pretty damned close to 1/2. The puzzle looks exactly as youd expect for a transparent lock (or as its also known, the Open Lock). It seems remarkable that the probability of having two boys changes from 1/3 to 13/27 when the birth day of one boy is stated yet it does, and its quite a generous difference at that. The problem is, that of the four family types BB, BG, GB, and GG, they only counted three of them but counted up to four. I see it differently (I can be that way). Therefore the probability of having BB is still 1/3. So who am I? Again two sets one black and one white in cubes of (10x10x10 with one additional tetracube). I think personnas Wikipedia excerpt (I havent read the whole page yet) may be identifying the assumption that I am making and that you arent (or perhaps the opposite you are assuming that the person is describing the children in some order). One is a boy born on a Tuesday. As for the Tuesday nonsense, if there was anything real to this at all, the whole of logic in this universe would be vastly different. Hinged dissections form the basis of his designs for reconfigurable robots, in which blocks hinged together in a chain can be made to fold into any three-dimensional shape. My price will include international shipping and all fees : you will pay only the cost of the lot . There are seven different possibilities here too, but one of them when both boys are born on a Tuesday has already been counted when we considered the first to be a BTu and the second on any day of the week. To play B-Cubed easily any time, you can add it directly to your phone as an app. If you have two children, and one is a boy, then the probability of having two boys is significantly different if you supply the extra information that the boy was born on a Tuesday. If the Smith family were selected as in the latter case, the answer to question 2 is 1/2. There are no other options. What is the probability I have two boys? (Assume uniformity over genders and days of the week.) Condition: Used. Now if you label the births with a subscript of 1 and 2 respectively it isnt hard to see that B1B2 is not the same ordered pair as B2B1, so you cannot throw it out to end up with only 6 outcomes after all. Remove all of the cubes on your way to the red one. pac-man. 13/27 is the answer to: So the other cup is 2/3 and you should swap. Tony Fisher Rubik-like Cubes. BG and GB are the same option in this scenario unless you specify the boy born on Tuesday was born first or second. Count it twice, giving 14/28 probability. The event was the Gathering for Gardner earlier this year, a convention held every two years in Atlanta, Georgia, uniting mathematicians, magicians and puzzle enthusiasts. What is the probability that there are two? I think that more clearly eliminates only the GG case. Add to cart. According to the idea presented, 66% of this group would have boys as the 2nd child. Gary Foshee. At its core the question simply asks, if you have a child, how likely is it that it will be a boy. Seems like nonsense to me, too. Period. Setteducati is a performing magician who curates the magic side of the G4G. Sorry but I forget the proper term for this. , 9 Salvatore is making some back-to-school packs for his teacher. Shell's Collection (Maintenance in Progress). Somebody says: "I have two children, (at least) one of them is a boy. ' said Foshee, deadpan. Once you remove the shackle from the frame, you can entirely disassemble the puzzle and leave yourself with an array of parts on the table. California-based mathematician Tom Rokicki showed some new patterns of mind-boggling ingenuity, including one which produced the image of the numeral 3, then the numeral 1, then 4 and continued writing out the digits of pi. The technicalities: a) if I remember correctly, the odds of girl vs boy are not 50/50, but more like 51/49. Well get to the answer later. Theres another thing to consider. In this game, you need to control the Math Man to eat all the ghosts. One is a boy born on a Tuesday. 4. The gathering is the worlds premier celebration of recreational mathematics. It's a great way to play without worrying about losing your game save data. If you add instances where you have two boys with at least one boys being born on Tuesday (13) to the instances where you would have two boys with neither being born on Tuesday (36) (total of BB (49) and compare it to all the instances where you have one girl and one boy (98) you get back to your 1/3 ratios. One is a boy born on a Tuesday.