41. Monty Hall Problem -- From MathWorld The monty hall problem is named for its similarity to the Let s Make a Dealtelevision game show hosted by Monty Hall. The problem is stated as follows. http://mathworld.wolfram.com/MontyHallProblem.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Applied Mathematics Game Theory Monty Hall Problem The Monty Hall problem is named for its similarity to the Let's Make a Deal television game show hosted by Monty Hall. The problem is stated as follows. Assume that a room is equipped with three doors. Behind two are goats, and behind the third is a shiny new car. You are asked to pick a door, and will win whatever is behind it. Let's say you pick door 1. Before the door is opened, however, someone who knows what's behind the doors (Monty Hall) opens one of the other two doors, revealing a goat, and asks you if you wish to change your selection to the third door (i.e., the door which neither you picked nor he opened). The Monty Hall problem is deciding whether you do. The correct answer is that you do want to switch. If you do not switch, you have the expected 1/3 chance of winning the car, since no matter whether you initially picked the correct door, Monty will show you a door with a goat. But after Monty has eliminated one of the doors for you, you obviously do not improve your chances of winning to better than 1/3 by sticking with your original choice. If you now switch doors, however, there is a 2/3 chance you will win the car (counterintuitive though it seems).

42. Quantum Information: Quantum Monty Hall Entangled Hbars. The Quantum monty hall problem. The monty hall problem is awellknown problem in statistics, which time and again leads to controversies http://www.imaph.tu-bs.de/qi/monty/

IMaPh Research Areas Quantum Information Monty Hall Simulation The Quantum Monty Hall Problem The Monty Hall problem is a well-known problem in statistics, which time and again leads to controversies because of its counter-intuitive solution . Here we consider a quantum version, which illustrates nicely some differences between classical and quantum information . As in the classical case a simulation helps to understand the solution. You will find on this site: An explanation of the quantum version of the problem, in parallel with a description of the classical version. Here we assume familiarity with basic quantum mechanics. A Simulation of the quantum version, in the form of a Java applet with instructions and some hints on what experiments you might try. A paper explaining the theory of the problem. A reminder of the solution of the classical problem , with links and references. A description of an even more quantum version, in which the prior information of the show master is encoded in an entangled state. The game Classical Quantum The basic setting of the problem is a game show. There is a prize hidden behind one of three doors, which the player (called P here) can get, if he opens the correct door. His opponent is the host of the show (called Q for quiz master), who basically tries to confuse the player.

43. IanG On Tap: The Monty Hall Problem The monty hall problem 7/21/2004 40552 PM. This one does the rounds every sooften, but it always tickles me. A friend recently blogged about it, http://www.interact-sw.co.uk/iangblog/2004/07/21/montyhall

IanG on Tap Ian Griffiths in Weblog Form RSS 2.0 Blog Navigation September (2005) (3 items) August (2005) (7 items) June (2005) (3 items) May (2005) (7 items) April (2005) (6 items) March (2005) (1 items) February (2005) (2 items) January (2005) (5 items) December (2004) (5 items) November (2004) (7 items) October (2004) (3 items) September (2004) (7 items) August (2004) (16 items) July (2004) (10 items) June (2004) (27 items) May (2004) (15 items) April (2004) (15 items) March (2004) (13 items) February (2004) (16 items) January (2004) (15 items) Blog Home RSS 2.0 Writing .NET Windows Forms in a Nutshell Mastering Visual Studio .NET WinFX in Detail column on O'Reilly's OnDotNet Other Sites Interact Software The Monty Hall Problem - 7/21/2004 4:05:52 PM This one does the rounds every so often, but it always tickles me. A friend recently

44. Monty Hall Problem: Information From Answers.com monty hall problem In search of a new car, the player picks door 3. The game hostthen opens door 1 to reveal a goat and offers to let the player. http://www.answers.com/topic/monty-hall-problem

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Best of Web Mentioned In Or search: - The Web - Images - News - Blogs - Shopping Monty Hall problem Wikipedia Monty Hall problem In search of a new car, the player picks door 3. The game host then opens door 1 to reveal a goat and offers to let the player pick door 2 instead of door 3. The Monty Hall problem is a puzzle in probability that is loosely based on the American game show Let's Make a Deal ; the name comes from the show's host Monty Hall . In this puzzle a player is shown three closed doors; behind one is a car, and behind each of the other two is a goat. The player is allowed to open one door, and will win whatever is behind the door. However, after the player selects a door but before opening it, the game host opens another door to reveal a goat. The host then offers the player an option to choose the other closed door. Does switching improve the player's chance of winning the car? With the assumptions explicitly stated below, the answer is yes The problem is also called the Monty Hall paradox , in the sense that the solution is counterintuitive, although the problem is not a logical self-contradiction. It has generated heated debate.

45. Marilyn Is Tricked By A Game Show Host Here are some quotes from Behind Monty Hall s Doors that the only personwho can answer this version of the monty hall problem is Monty Hall himself. http://www.wiskit.com/marilyn.gameshow.html

Marilyn is tricked by a game show host Marilyn is Wrong Herb Weiner by Marilyn vos Savant is a column in Parade Magazine , published by PARADE, 711 Third Avenue, New York, NY 10017, USA. According to Parade, Marilyn vos Savant is listed in the "Guinness Book of World Records Hall of Fame" for "Highest IQ." In her Parade Magazine columns of September 9, 1990, February 17, 1991, and July 7, 1991, Marilyn discusses a gameshow in which the contestant is given a choice of one of three doors, behind one of which is a prize. The reader asks if, after the contestant chooses a door, the host opens a different door, revealing no prize, and offers the contestant the opportunity to switch doors, whether the contestant should switch or not. Marilyn replies that the contest should switch, because the second door has a 2/3 chance of winning. Sorry, Marilyn Marilyn, there's nothing wrong with your math. As you noted, math answers aren't determined by votes. But TV ratings are! What could possibly have justified your assumption that the game show host offers every contestant the same choice? The initial question described only a single incident. If I were the game show host, and you were the contestant, I'd offer you the option to switch

46. Sci.math FAQ: Monty Hall Problem sci.math FAQ monty hall problem 1994 Version 6.2 The monty hall problemThis problem has rapidly become part of the mathematical folklore. http://www.faqs.org/faqs/sci-math-faq/montyhall/

Usenet FAQs Search Web FAQs Documents ... RFC Index sci.math FAQ: Monty Hall problem There are reader questions on this topic! Help others by sharing your knowledge Newsgroups: sci.math alopez-o@neumann.uwaterloo.ca alopez-o@barrow.uwaterloo.ca Tue Apr 04 17:26:57 EDT 1995 Rate this FAQ N/A Worst Weak OK Good Great Related questions and answers Usenet FAQs Search Web FAQs ... RFC Index Send corrections/additions to the FAQ Maintainer: alopez-o@neumann.uwaterloo.ca Last Update June 15 2004 @ 00:31 AM

47. The Monty Hall Problem The monty hall problem involves a classical game show situation and is named The monty hall problem became the subject of intense controversy because of http://www.ds.unifi.it/VL/VL_EN/games/games6.html

Virtual Laboratories Games of Chance 6. The Monty Hall Problem Statement of the Problem The Monty Hall problem involves a classical game show situation and is named after Monty Hall , the long-time host of the the TV game show Let's Make a Deal . There are three doors labeled 1, 2, and 3. A car is behind one of the doors, while goats are behind the other two: The rules are as follows: The player selects a door. The host selects a different door and opens it. The host gives the player the option of switching from her original choice to the remaining closed door. The door finally selected by the player is opened and she either wins or loses. The Monty Hall problem became the subject of intense controversy because of several articles by Marilyn Vos Savant in the Ask Marilyn column of Parade magazine, a popular Sunday newspaper supplement. The controversy began when a reader posed the problem in the following way: Marilyn's response was that the contestant should switch doors, claiming that there is a 1/3 chance that the car is behind door 1, while there is a 2/3 chance that the car is behind door 2. In two follow-up columns, Marilyn printed a number of responses, some from academics, most of whom claimed in angry or sarcastic tones that she was wrong and that there are equal chances that the car is behind doors 1 or 2. Marilyn stood by her original answer and offered additional, but non-mathematical, arguments. 1. Think about the problem. Do you agree with Marilyn or with her critics, or do you think that neither solution is correct?

48. The Monty Hall Problem This has come to be known as the monty hall problem. It is very well known inmathematical and statistical circles because the correct answer to the problem http://www.visi.com/~sgrantz/july/monty.html

Home July 1997 -> Monty Hall Problem The Monty Hall Problem Monty Hall hosted a game show around 25 years ago in which he fast-talked people into making deals for cash and prizes. Audience members wore ridiculous costumes, and at the end of the show, Monty would wander through the melange of clowns, chickens, and chefs, offering quick cash if selected people could produce a desired item. "I'll give you $40 if you have hairspray in your purse," Monty would ask some woman in a green bodysuit with foam flower petals surrounding her head. It was a laugh riot. The centerpiece of the show, however, was "The Deal". Monty would pick someone from the audience, give them cash, the tell them that behind one of three doors was a lovely gift. They could keep the cash, or pick one of the doors. After picking, say, door #1, the real fun began. Without opening door #1, Monty would reveal the contents of door two, usually a lovely Amana kitchen appliance. Then he would ask if they wanted to switch from door #1, contents unknown, to the remaining door, #3. This has come to be known as the Monty Hall Problem. It is very well known in mathematical and statistical circles because the correct answer to the problem is counterintuitive. You should always switch.

49. Monty Hall Problem -- Facts, Info, And Encyclopedia Article monty hall problem. Categories Paradoxes, Mathematical recreations and puzzlesThe monty hall problem is a puzzle in (A measure of how likely it is that http://www.absoluteastronomy.com/encyclopedia/m/mo/monty_hall_problem.htm

Monty Hall problem [Categories: Paradoxes, Mathematical recreations and puzzles] The Monty Hall problem is a puzzle in (A measure of how likely it is that some event will occur) probability that is loosely based on the (A native or inhabitant of the United States) American (A television or radio program in which contestants compete for awards) game show (Click link for more info and facts about Let's Make a Deal) Let's Make a Deal ; the name comes from the show's host (Click link for more info and facts about Monty Hall) Monty Hall . In this puzzle a contestant, say Jane, is shown three closed doors; behind one is a car, and behind each of the other two is a goat. Jane is allowed to open one door, and will win whatever is behind the door she opens; however, after Jane has selected a door but before she actually opens it, the host (who knows what is behind each door) opens another door to show that there is a goat behind it. The host then offers Jane the opportunity to change her mind and switch to the other closed door. The host knows what is behind each door, always opens one of the two remaining doors to reveal a goat, and always offers the chance to switch. Does Jane improve her chance of winning the car by switching or does it make no difference? The question has generated heated debate. The difficulty arises when someone assumes that Monty is choosing elements at random, or making the offer more often (or only) depending on his knowledge of the contestant's original choice. As stated, he

50. Empirical Solution Of The Monty Hall Problem -- Facts, Info, And Encyclopedia Ar of the (Click link for more info and facts about monty hall problem) MontyHall problem by ((computer Approximate solution of the monty hall problem http://www.absoluteastronomy.com/encyclopedia/e/em/empirical_solution_of_the_mon

Empirical solution of the Monty Hall problem [Categories: Paradoxes, Mathematical recreations and puzzles] The following (Click link for more info and facts about Perl) Perl program computes an approximate solution of the (Click link for more info and facts about Monty Hall problem) Monty Hall problem by ((computer science) the technique of representing the real world by a computer program) simulation . Two strategies are simulated: stick with initial choice every time, or switch from initial choice every time. The program performs a number of games and counts how many times each strategy wins the game. The result of the simulation almost always shows that the switch strategy wins about twice as many times as the stick strategy. This is empirical evidence that switching is a better strategy in this game. 1. !/usr/bin/perl 2. Approximate solution of the Monty Hall problem 3. Use -v to see each game. (default: off) 4. Use -i # to set number of iterations. (default: 3000) use strict; my $iterations = 3000; # How many games to play my $verbosity = 0;

51. Analysis Of The Monty Hall Problem monty hall problem Block Swapping Problem. search by FreeFind Polyominoes Home Kevin s Home Page. Analysis of the monty hall problem http://kevingong.com/Math/MontyHall.html

Kevin's Math Page Home Contact Home Research ... Contact Topics: Polyominoes Egyptian Fractions Graceful Graphs 16 Puzzle ... Block Swapping Problem search by FreeFind Polyominoes Home Kevin's Home Page Analysis of the Monty Hall Problem Kevin Gong March 17th, 2003 There are numerous web pages devoted to discussion and analysis of the Monty Hall problem. I hope to add something new and interesting to the discussion with an analysis of a more interesting problem. For those of you living in a mathematical cave, I'll briefly explain the problem and very little on the controversy. In 1991, Parade Magazine published a column "Ask Marilyn" in which Marilyn vos Savant replies to a reader's question: "Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the other doors, opens another door, say No. 3, which has a goat. He then says to you, 'Do you want to pick door No. 2?' Is it to your advantage to take the switch?" Marilyn replied that the answer was yes, and there was a big uproar and mathematicians from across the country attacked her. I'll spare you the details. You can do a web search on that if you're interested. I'm more interested in the mathematics.

52. Monty Hall Problem - Definition Of Monty Hall Problem In Encyclopedia In search of a new car, you pick door number 2, Monty then shows you the goatbehind door number 1 and asks if you d like to switch to door number three. http://encyclopedia.laborlawtalk.com/Monty_Hall_problem

Add to Favorites General Encyclopedia Legal ... Law forum Search Word: Visit our Law forums Labor Law Accidents Law Bankruptcy Law Business Law ... Tax Law In search of a new car, you pick door number 2, Monty then shows you the goat behind door number 1 and asks if you'd like to switch to door number three. You have better odds if you do. The Monty Hall problem is a puzzle in probability that is loosely based on the American game show Let's Make a Deal ; the name comes from the show's host Monty Hall . In this puzzle a contestant is shown three closed doors; behind one is a car, and behind each of the other two is a goat. The contestant is allowed to open one door, and will win whatever is behind the door he opens; however, after the contestant has selected a door but before he actually opens it, the host (who knows what is behind each door) opens one of the other doors to show that there is a goat behind it, and asks the contestant whether they want to change their mind and switch to the other closed door. Does the contestant improve their chance of winning the car by switching or does it make no difference? The question has generated heated debate. As the solution appears to contradict elementary ideas of probability and common sense, it may be regarded as a

53. Phoenixrealm » Monty Hall Problem monty hall problem. July 23rd, 2005. I was reading the Wikipedia today, andstumbled across something that really interested me the monty hall problem. http://phoenixrealm.com/2005/07/23/monty-hall-problem/

Home About Images Contact ... Monty Hall Problem July 23rd, 2005 I was reading the Wikipedia today, and stumbled across something that really interested me: the Monty Hall Problem Esentially the idea is that you have three choices of which two are wrong and one is right. You select which one you want, not knowing what it is, and then one of the two wrong answers are revealed to you. You are then given the choice to change your answer, and by doing so, you have actually improved your odds at winning. You see this on game shows all the time, and the example used at Wikipedia is: In this puzzle a player is shown three closed doors; behind one is a car, and behind each of the other two is a goat. The player is allowed to open one door, and will win whatever is behind the door. However, after the player selects a door but before opening it, the game host opens another door revealing a goat. The host then offers the player an option to switch to the other closed door. The way it works is that when you were given three choices, you were more likely to chose the wrong item (66% chance of being wrong), so if you bet on that fact, when you are left with two choices, moving over to the one you did not chose, is more likely the correct choice. I would love to create a simple program to test the validity of this because it really messes with my head. I love it! I also think it says so much about life.

54. Monty Hall Problem And Intuitive Solutions In the Classical monty hall problem, the StayStrategy succeeds with 1/3 The Modified monty hall problem is actually three problems considered in http://www.aggressivesoftware.com/misc/montyhall/

Home Resume Projects Research ... Photos Monty Hall Problem and Intuitive Solutions Foreword Dear DES group: This problem bothered me all night, but I finally came to grips with it during my swim this morning. Classical Problem There are three doors. Two hide nothing. One hides a car. In phase 1, you pick a door. Monty (knowing where the car is) opens a door that does not hide a car and that you did not pick. In phase 2, you may stay with your chosen door (StayStrategy) or you may change your guess to the one remaining door (SwapStrategy) . If you've picked the door that hides the car, you win the car. The Truth In the Classical Monty Hall problem, the StayStrategy succeeds with 1/3 probability, and the SwapStrategy succeeds with 2/3 probability. Hand Wavy Justification Imagine that there are 100 doors. You choose one. Knowing where the car is, Monty Hall opens 98 doors (other than your pick) that don't have the car. It is intuitively clear that your door has low probability of success, while the swap door has high probability of success. Modified Problem Imagine the same game, except Monty Hall doesn't know where the car is. After you pick a door in phase 1, he randomly reveals one of the remaining two doors. Now consider the situation where (by chance) he does not reveal the car. Should you stay or swap? Note: this problem only considers the situation when Monty Hall (by chance) has opened a door that does not hide the car.

55. Nota Bene - The Monty Hall Problem - There Are Three Doors On Stage, Labeled A, Nota Bene The monty hall problem - There are three doors on stage, labeled A,B, and C. http://www.davidpbrown.co.uk/nota-bene/monty-hall-problem.html

The Monty Hall problem This rather interesting problem arises from a game show, Monty Hall is the host.. There are three doors on stage, labeled A, B, and C. Behind one of them is a pile of money; behind the other two are goats. You get to choose one of the doors and keep whatever is behind it. Let's suppose that you choose door A. Now, instead of showing you what's behind door A, Monty Hall slyly opens door B and reveals... a goat. He then offers you the option of switching to door C. Should you take it? (Assume, for the sake of argument, that you are indifferent to the charm of goats.) Counterintuitively enough, the answer is that you should switch, since a switch increases your chance of winning from one-third to two-thirds. Why? When you initially chose door A, there was a one-third chance you would win the money. Monty's crafty revelation that there's a goat behind door B gives no new information about what's behind the door you already chose you already know one of the other two doors has to conceal a goat so the likelihood that the money is behind door A remains one-third. Which means that, with door B eliminated, there is a two-thirds chance that the money is behind door C. Still not convinced? Perhaps it will help if you look at the game from Monty's perspective. For him, the game is very simple. No matter what door the contestant picks initially, his job is to reveal a goat and ask the contestant if they want to switch.

56. The Monty Hall Problem The monty hall problem. You are a player on a gameshow. Before you are threedoors, behind each is either a goat or a car. There are two goats and one car. http://www.interfootball.co.uk/monty/default.htm

Interfootball Problem Mate Monty Hall Big Chain Report It Get a Date The Monty Hall Problem You are a player on a gameshow. Before you are three doors, behind each is either a goat or a car. There are two goats and one car. Select a door and one of the remaining doors will open to reveal a goat. Click on door Statistics (0) If Stuck If Changed Overall Did Stick Did Change Home Interfootball Problem Mate Monty Hall Big Chain Report It Get a Date Contact pw@interfootball.co.uk

57. Monty Hall Problem - Enpsychlopedia The monty hall problem is a puzzle in probability that is loosely based on the The problem is also called the Monty Hall paradox, in the sense that the http://psychcentral.com/psypsych/Monty_Hall_problem

home resource directory disorders quizzes ... support forums Advertisement ( Monty Hall problem Missing image Monty-hall.png In search of a new car, the player picks door 3. The game host then opens door 1 to reveal a goat and offers to let the player pick door 2 instead of door 3. The Monty Hall problem is a puzzle in probability that is loosely based on the American game show Let's Make a Deal ; the name comes from the show's host Monty Hall . In this puzzle a player is shown three closed doors; behind one is a car, and behind each of the other two is a goat. The player is allowed to open one door, and will win whatever is behind the door. However, after the player selects a door but before opening it, the game host opens another door to reveal a goat. The host then offers the player an option to choose the other closed door. Does switching improve the player's chance of winning the car? With the assumptions explicitly stated below, the answer is yes The problem is also called the Monty Hall paradox , in the sense that the solution is counterintuitive, although the problem is not a logical self-contradiction. It has generated heated debate. Contents showTocToggle("show","hide")

58. Mudd Math Fun Facts: Monty Hall Problem monty hall problem. Figure 1 Figure 1. Here s a problem that makes the roundevery few years, and each time, it is hotly debated. You are on a game show. http://www.math.hmc.edu/funfacts/ffiles/20002.6.shtml

hosted by the Harvey Mudd College Math Department Francis Su Any Easy Medium Advanced Search Tips List All Fun Facts Fun Facts Home About Math Fun Facts ... Other Fun Facts Features 181937307.184684 Fun Facts viewed since 20 July 1999. Francis Edward Su From the Fun Fact files, here is a Fun Fact at the Medium level: Monty Hall Problem Figure 1 Here's a problem that makes the round every few years, and each time, it is hotly debated. You are on a game show. You are presented with a choice of 3 doors: behind one is a luxury car, and behind the other two are nothing. The host asks you pick one of the doors. After you do this, as part of the game he opens one unpicked doors which he knows is empty. There are now only the door you picked and one remaining door which are unopened. You are asked if you would like to switch your choice. Should you switch? Presentation Suggestions: Another version of this problem uses cards in a game called "three-card monte", often played by scam artists on the streets of New York who prey on easily-duped tourists. The Math Behind the Fact: The answer is YES, you should switch, because the probability that you will find the car by doing so is 2/3. This is because the probability that you picked the correct door in the first place does

59. Science Central - The Infamous Monty Hall Problem Monty Hall (Populatiry ) Contains a introduction to the problem, A NewApproach to the monty hall problem (Populatiry ) Introduces the problem and http://www.sciencecentral.com/site/493244

Friday, 16 September, 2005 Home Submit Science Site Set as Homepage Add to Favorite ... Contact search for Directories Agriculture Anomalies and Alternative Science Astronomy Biology ... Technology Category: Science Math Recreations Famous Problems ... REPORT BROKEN LINK The Infamous Monty Hall Problem Populatiry: Details document.write(''); Short introduction for beginners. URL Title The Infamous Monty Hall Problem Description Category: Traffic Analysis document.write(''); document.write(''); document.write(''); Related sites The Knight's Tour Links Page (Popularity: ): The goal is to travel with a knight around the ... U of T Mathematics Network (Popularity: ): Includes interactive games, problems and puzzles including the Monty Hall ... Monty Hall Dilemma (Popularity: ): Includes the original question posed to Marylin vos Savant about ... Mathnet : The Car and the Goats (Popularity: ): Introduction to the problem and the controversy. As well as ... Marilyn is Tricked by a Game Show Host (Popularity: ): Comments on Marilyn vos Savant response to the question about ...

60. BBC - H2g2 - The Monty Hall Problem h2g2 is the unconventional guide to life, the universe and everything, a guidethat s written by visitors to the website, creating an organic and evolving http://www.bbc.co.uk/dna/h2g2/A1138655

@import url('/includes/tbenh.css') ; Home TV Radio Talk ... A-Z Index Friday 16th September 2005 Text only Guide ID: A1138655 (Edited) Edited Guide Entry SEARCH h2g2 Advanced Search New visitors: Returning members: BBC Homepage The Guide to Life The Universe and Everything 3. Everything Deep Thought Psychology ... Mathematics Created: 22nd September 2003 The Monty Hall Problem Front Page What is h2g2? Who's Online Write an Entry ... Help Like this page? Send it to a friend! Probability is a branch of mathematics that most people have an instinctive feel for. Our instinctive feel is often wrong. One of the best examples where common sense is at odds with Probability Theory is known as 'The Monty Hall Problem'. When the mathematical solution is given, people are convinced it is wrong. Mathematicians have almost come to blows in discussing this problem. The Problem The problem is inspired by an American game show, Let's make a Deal which ran on NBC throughout the 1960s and . The host, Monty Hall, would often give contestants a chance to change their mind. The problem as outlined here is not the way Monty actually behaved on the show, but is interesting nonetheless. In the Monty Hall Problem, there are three identical doors. Behind one of the doors is a valuable prize, say a dream holiday. Behind the other two doors there is nothing. You are allowed to choose one door. If you choose the right one, you get the prize. But before the door is opened, the host (and let's call him Monty) proceeds to open one of the other two doors and shows you that there is nothing behind it. Now you are given the option of sticking with your original choice or changing your mind. What should you do?

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