Once you know one child is a boy, then there are only four equally likely possibilities for the second childa younger boy, an older boy, a younger girl or an older girl. When somebody says to you"I have two children, at least one of them is a boy", who is to say that they weren't using exactly the same rule as me, picking one child at random and revealing its gender. Q2) Say I peek in the box, and tell you that there is (at least) one bronze coin inside. One should take in account what instances they are excluding as much as what they are including. In two of these cases we get two boys, so the probability of having two boys is 2/4, ie 0.5. forget about twinsone is always a little older than the other. The issue is the question that was posed, which was a slight of hand. Solve the following. To say otherwise means that you must also have a BB and a BB as your options to go with BG and GB, where B is the unspecified child, leaving you with, wait for it, a 50-50 chance once again. Pac-Man Puzzle cube Twist turn brain Teaser 2 1/4" by 2 1/4". Having been trying to get one of these for a while, and missing them at auction Im happy to have picked one of these up. If I see a tail first I say"At least one is a Tail". Better yet, buy one of his books for your kid. Period. The answer could be 13/27 or 1/2, but it can't be 1/3. Mathematicians are especially fascinated by sets of tiles that can only produce a pattern that never repeats. credit and sources back to your website? If the answer was really only 1/3 for the 2nd child being a boy, then there is a 2 out of 3 chance that that child is a girl. This was first presented in 2000 at the IPP Los Angeles and although. They require that, to get the 1/3 answer. Remove all of the cubes on your way to the red one. That is, potentially what are the probabilities of what could have happened? Cubo de rubik , coleccionismo , Rubiks cube , todo acerca del cubo rubik, grcias por tu visita. If you want more details, you can read Wikipedias article on this. the people who are confused and cant see why it s not just 50/50 you are assuming that the FIRST child is a boy born on a tuesday, but the question says that ONE OF THE TWO (you dont know which) is a boy born on a tuesday. He was displaying a copy of a puzzle he had invented called Jigazo, currently the top-selling puzzle in Japan. On average, 100 have 2 boys, 100 have 2 girls and 200 have a boy and a girl (100 had a boy then a girl, and 100 had a girl then a boy). There are then 27 (rather than 28) allowable combinations of boy / girl / day, 13 of which (rather than 14) are boys. SpaceX launch cancelled: Why didn't Elon Musk's Starship blast off? Here's the entire text of a talk given at math, magic, and puzzle gathering (attendees included Stephen Wolfram and John Horton "Game of Life" Conway) by Gary Foshee: I have two children. The bold emphasis is mine, indicating what I consider to be the key to the 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. The question states that one child is a boy. CHECK OUT HIS VIDEO --- https://youtu.be/uaq7H2r1P_s (SPOILERS DONT WATCH THE VIDEO YET). When they count families with at least one boy, they count four of them: two where the older child is a boy and the younger is either a boy or a girl, and two where the younger child is a boy and the older is either a boy or a girl. In this game, you need to control the Math Man to eat all the ghosts. But Ill admit I didnt enjoy all those matrix maths in 5 function calculator days. I figured, its 50/50 and the Tuesday was a distractor. But thats not what was stated. But I think that devolves into a very simple and mechanical exercise. 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. One is a boy. Ive been slowly adding to my collection of trick locks over the last few years, and first saw the Transparent Lock by Gary Foshee a couple of years back, but sadly missed out back then as they sold incredibly quickly. Now aged 29, he presented to the gathering some typefaces that he had invented as a result of his academic work in computational geometry. The puzzle does NOT state that the first child was a boy. If youre looking for a challenge on the order of a Popplock, then youll want to look elsewhere as I feel you will probably be disappointed. Includes Address (20) Phone (3) Email (6) See Results. By sheer coincidence, every one of them has a different combination of (gender,day)x(gender,day) for their two children. Greg Frederickson Stacked Triangles. Why isn't the chance of the other child being a boy simply 50-50, and what on earth . We get 7/14 or . Either the boy specified was born first in which case the only options are then BB or BG, or the boy specified was born second, in which case the only options are GB or BB. Of the 196 permutations Sex1Day1:Sex2Day2, how many include at least one BTu? Fast & Free shipping on many items! Tiling is a major theme in recreational mathematics possibly because as well as being conceptually rich it is also aesthetically gratifying. Either one of two cases is possible. The gathering is the worlds premier celebration of recreational mathematics. So you are excluding taking 25% of first set and 50% of second set. Imagine there were two NFL games today and you dont know how they ended, but that I tell you that one of the games was won by the team that won the coin toss. But such a change can only happen if useful information is gained, and it has not. I am not a mathematician so cannot express this in mathematical terms, but I am still sure it is right! Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. Or if Tuesday births were not 50/50 with a margin of confidence. Listed here are some of my puzzles that can be found in TwistyPuzzles' database. As for your 3/7, once again you are taking a subset of the BB,GB,BG problem. In this case the critical assumption is how Mr. Smiths family was selected and how the statement was formed. He believes that cellular automata can recreate the universe and is trying to find the ones that do. When localizing the game for North America and Europe, Namco realized that the game's formula was a great fit for the Pac-Man . 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. 2x2x2; 3x3x3; 3x3x3 (Picture) 4x4x4; 5x5x5; 6x6x6 & Up; Six-Sided. 1. So the answer is 13/27, which is very different from 1/3. As a melting pot of outside-the-box abstract thinking, this gathering is one of a kind. Gary Foshee: Craftsman: Gary Foshee: Category: Take-Apart: Material: Aluminum & Steel: The objective is to put all of the parts inside the cube using only the tools provided. We seem to be going in circles, and I come back to my original point. This puzzle can be found in collections of these members: Online since 2002. is off base in this example. But you were forced to interpret words to identify the underlying mathematical equations. What is the chance they have two boys. b) genetics matter; if you have a boy, you are more likely to have another boy. She did not and does not. How to play B-Cubed on your phone. The game's objective is to prevent the falling blocks from stacking to the top of the screen by placing them in rows for them to disappear. "I have two children, one of them is a boy born on a TUESDAY." (in contrast to the other boy who was born on a WEDNESDAY). New Scientist consultant Jeff Hecht has written an assessment of his career on our CultureLab blog. But 1/3 is not the only valid answer. To get any other answer requires an ambiguity to be exploited in the statement of the problem, as well as confusing dependence and independence of the two births as discrete events. Our possible situations are: Summing up the totals, there are 7 + 7 + 7 + 6 = 27 different equally likely combinations of children with specified gender and birth day, and 13 of these combinations are two boys. After all, there are only two sexes and its 50/50 the second will be a boy. Puzzle World 1997-2017 by John . . It consisted of the following three sentences: "I have two children. Of these 27 families 14 include 1 girl (7 older sisters, 7 younger). With your permission we and our partners may use precise geolocation data and identification through device scanning. Grumpy Old Man Archive. Browse. 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 Jigazo which will be released in Europe and the US later this year was a product of this traffic. If the Smith family were selected as in the latter case, the answer to question 2 is 1/2. Not so much. One is a boy born on a Tuesday. First, why they are wrong. Gary Foshee, a collector and designer of puzzles from Issaquah near Seattle walked to the lectern to present his talk. My expectation, based not on math, but on framing of the Boy/Tuesday problem, that it was a random selection of a family, and that Boy/Tuesday were observations about that random sample. Well, it has everything to do with it. And then he stepped down from the stage. It contains 300 identically shaped pieces that are all a different shade of blue, and all have a unique symbol on the back. Today I'm going to attempt to solve this very rare Level 10 Packman Cube Puzzle by Gary Foshee. One is a boy born on a Tuesday. I think the application of Bayes theorem is incorrect because I dont think the two events satisfy the definition of being independent, but Ill have to check the textbook tomorrow to be sure. Gary Foshee created a popular probability puzzle that goes like this: "I have two children. 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. 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. By sheer coincidence, every one of them has a different combination of (gender,day)x(gender,day) for their two children. Period. The two disciplines are happy bedfellows: both exhibit a wonder at the structure of the world, and seek playful ways to subvert it. * In an episode of 'The Infinite Monkey Cage' on BBC Radio 4, Richard Wiseman posed the puzzle in minimalist form: "he has two children, one of them is a boy", leaving out the "at least", just as Gary Foshee did. Lets list the equally likely possibilities of children, together with the days of the week they are born in. What is the probability I have two boys?. It is a rare puzzle, it is an old puzzle, it is rated a 10 by Chris Ramsey. At the opposite end of the age spectrum was Neil Bickford, aged 12, a mathematics blogger from San Jose, California. 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 gathering is the worlds premier celebration of recreational mathematics. (LogOut/ Going back to one of my previous posts, would it change anything for you if the wording was, at least one is a boy? You need to solve the mathematical formulas and eat the ghosts. 00 - help - There are many more free arcade games to play! We misinterpret the original question as What are the chances of me having another boy. Always use your own judgement when buying or selling an item. Designed by Joshua Socolar, a physicist from Duke University in Durham, North Carolina, and Joan Taylor from Burnie, Tasmania, Australia, it looks like a cross between a snowflake and a small craft from an early Star Wars movie. Richard shares a variation (imagined by Gary Foshee) which it find the counter-intuitive: I have two children. Change), You are commenting using your Facebook account. Gardner initially gave the answers 1/2 and 1/3, respectively; but later acknowledged[1] that the second question was ambiguous. 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