Locker Problem Answer

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• [GET] Locker Problem Answer | free!

  Write a program to find your answer. Hint: Use an array of Boolean elements, each of which indicates whether a locker is open true or closed false. Initially, all lockers are closed.

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• [FREE] Locker Problem Answer

  As written then. The options here are binary; the locker is either opened or closed. So any random locker will remain open after the th student if n is an odd number. So we just need to find numbers between 1 and that have an odd number of factors....

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• Top Exams 2021

  If instead you meant that the 1st student opens all of the lockers, then the answer is just the locker numbers that are perfect squares, so

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  Gear-obsessed editors choose every product we review. We may earn commission if you buy from a link. How we test gear. Feb 28, Kory Kennedy using Illustration Copyright csaimages. Student 1 will open it, since student 1 opens every locker. Student 2 will then close it, since student 2 closes every even locker and 24 is even. Student 3 will open it and then student 4 will shut it, since 24 is a multiple of both 3 and 4. Student 5 will pass it by since 24 is not a multiple of 5. Thus, locker 24 will have its status changed by students 1, 2, 3, 4, 6, 8, 12, and Now, how does this lead us to figure out which lockers are opened at the end? Locker 1, which has one factor, will clearly be open at the end, since the only student who touches it is the first student, who opens it. Locker 2, with two factors, will be closed, since the only two students to touch it are student 1, who opens it, and then student 2, who closes it. Locker 3, also with two factors, will also be closed at the end.

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• The Locker Game

  On the other hand, locker 4, which has three factors 1, 2, and 4 , will be open, shut, and then open again. This line of thinking leads us to the conclusion: Only those lockers with an odd number of factors will be left open at the end of the prank. So which numbers have an odd number of factors? Consider that a factor is an integer that, when multiplied by another integer, produces the number of interest. Since factors come in pairs, most numbers have an even number of factors. The only exception occurs when factors are paired with themselves. In this case, 4 is paired with itself to produce the number Thus, 16 has an odd number of factors: 1, 2, 4, 8, Factors are only ever paired with themselves in the case of perfect squares, which means that perfect squares are the only numbers with an odd number of factors!

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• [DOWNLOAD] 100 Locker Math Problem Answer | Free!

  Problem 1 To start with, we can simply begin walking through process by hand. Locker 1 will begin closed, then the 1st person will come in an open it. After that, no one touches the 1st locker so we know it stays open. Locker 2 is opened by the 1st person, closed by the 2nd and it stays closed. Locker 3 is opened by the 1st person, left alone by the 2nd and then closed by the 3rd. This is going to get tedious if I keep explaining in words. Lets use a table. This is also going to get tedious if I want to do this for lockers and students. We definitely need to find a pattern. My next step was put together a lazy little Matlab script to do the same exact thing as my table. See here. There is definitely a pattern! Notice those open lockers form the bands you see in the picture.

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• The Locker Problem

  So why do some end up open and some end up closed? The easiest way to see why is to consider what happens to a single locker. For example, think about locker When does it change state? Obviously, person 1 opens the locker, person 2 closes it, person 3 opens it, person 4 closes, person 5 does nothing, etc. Notice that if the locker number, 24, is divisible by the person number, then the state changes: The number 24 has 8 factors, that is, 8 numbers that divide evenly into it. So the key is that any locker number with an even number of factors will end up with closed and any with an odd number will end up open. So what numbers have an odd number of factors?

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• Natural Blogarithms

  Math Math brain teasers require computations to solve. Math Suppose you're in a hallway lined with closed lockers. You begin by opening every locker. Then you close every second locker. Then you go to every third locker and open it if it's closed or close it if it's open. Let's call this action toggling a locker. Continue toggling every nth locker on pass number n. After passes, where you toggle only locker , how many lockers are open? Answer Answer: 10 lockers are left open: Lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, and Each of these numbers are perfect squares. This problem is based on the factors of the locker number. Each locker is toggled by each factor; for example, locker 40 is toggled on pass number 1, 2, 4, 5, 8, 10, 20, and That's eight toggles: open-closed-open-closed-open-closed-open-closed.

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• The Locker Problem

  The only way a locker could be left open is if it is toggled an odd number of times. The only numbers with an odd number of factors are the perfect squares. Thus, the perfect squares are left open. For example, locker 25 is toggled on pass number 1, 5, and 25 three toggles : open-closed-open.

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• The Locker Problem....?

  Presentation on theme: "The Locker Problem. There are lockers, all shut and unlocked, and students. If the locker is open the student shuts it, and if the locker is closed the student opens it. At the end, which lockers will be open and which will be closed? So, there is an open locker door at every square number. How many square numbers are there between 1 and ? Through a little trial and error, you'll find that is the last square number less than So, there are 31 open doors the last one occurring on the door numbered or A factor is a number that divides another number evenly with no remainder. For example, 8 has an even number of factors, namely, 1, 2, 4, and 8. But, 9 has an odd number of factors, namely, 1, 3, and 9.

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• The 100 Locker Problem

  In fact, all numbers except the square numbers have an even number of factors. Take any locker number, 40, for example. Its state open or closed is changed for every student whose number in line is a factor of the locker number. So, write out all the factors of 40, like this: Student Leaves locker 40 1 Open 2 Closed 4 5 8 10 20 40 13 Like all other lockers numbered with non-square numbers, it ends up closed after all the students have gone through the line because it has an even number of factors. Student Leaves locker 16 1 Open 2 Closed 4 8 16 Locker 16 remains open because it has an odd number of factors. You can now conclude that all the doors with non-square numbers on them will remain closed because only square numbers have an odd number of factors. The numbers of the open doors are listed below.

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• Can You Solve The ‘1,000 School Lockers’ Riddle?

  You can put this solution on YOUR website! There is no real formula for this type of problem. You need to break this problem down into smaller parts, and then generalize a bigger picture from those parts. Lets say we only have 10 people and 10 lockers. If person 1 opens all of the lockers, they're all open. Now person 2 goes, and all of the even numbered lockers are shut. Now it's 3's turn: locker 3 is shut, locker 6 is open again, and 9 is shut. Four takes a shot and locker 4 and 8 are reopened. Students 6, 7, 8, and 10 only shut locker 6, 7,8, and 10 respectively; while person 9 opens locker 9. So if we look at say locker 6, person 1 opens it, person 2 closes it, person 3 opens it, and finally person 6 closes it. So there are 4 people who interact with it notice how its an even number. While with locker 4, only students 1,2,4 touch it, and it stays open. So by this reasoning, if an even number of people touch it, it stays closed.

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• The Locker Problem Answer ?

  If an odd number of people touch it, it stays open. To find out how many people touch it, we simply find the number of factors the number has. With 6 there are 4 factors: 1,2,3,6. The four factors simply cancel each other out one action of opening is undone by another action of closing. While the number 4 has 3 factors: 1,2,4. These factors dont cancel so it stays open.

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• The Locker Problem – The Math Doctors

  It turns out that every number, except the perfect squares, has an even number of factors. All of these factors are paired up, which means there are an even number of factors. So there are only 3 factors in this number. This is true for all perfect squares, since there's always a repeated factor of the square root value. So every perfect square locker number will remain open because they have an odd number of factors. This makes it easier to count the number of open lockers since we only have to find perfect squares.

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• Lockers Puzzle - Programmer And Software Interview Questions And Answers

  However, you can still earn stars Imagine you are at a school that still has student lockers. There are lockers, all shut and unlocked, and students. Suppose the first student goes along and opens every locker. The second student shuts every other locker beginning with number 2. The third student changes the state of every 3rd locker.

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• 100 Closed Lockers

  So if the locker is open the student shuts it, and if the locker is closed the student opens it. The fourth student changes the state of every 4th locker. This continues until all students have followed the pattern with these lockers. Which lockers will be open and which will be shut after all students have passed through? Explain how you found your answer.

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• The Locker Problems Solved | Natural Blogarithms

  September 16, This is probably one of the best math problems I give my fifth grade students. It goes like this: There are lockers in the long front hall of our school. Each August, the custodians add a fresh coat of paint to the lockers and replace any of the broken number plates. The lockers are numbered from 1 to When the students arrive on the first day, they decide to celebrate the start of the school year with our school tradition. The first student inside runs down the hall opening all of the lockers. The second student runs down the hall closing every second locker, beginning with locker number 2. The third student reverses the position of ever third locker, beginning with locker number 3. If the locker is open, she closes it. The fourth student changes the position of every fourth locker, beginning with number 4. This continues until the th student has a turn, changing the position of the th locker. At the end of this ritual, which locker doors are open?

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• Lisa Winer: Can You Solve The Locker Riddle? | TED Talk Subtitles And Transcript | TED

  Why are the open lockers left open? Which patterns emerged in your work? After a week of working on this problem with their partner, they write up what they discovered on posters. I have them include these four sections: 1. Restate the problem 3. Answer 4. Also, students ask comments or give feedback to the groups that present. Here are some of their posters.

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• Unraveling The Locker Problem

  I have often told people that, believe it or not, they could find the answer by searching the Llocker Dr. But I prefer to give them a reference to one of the answers in which we gave only hints, because this is a fun problem to discover the answer for yourself. Tiny hints Here is a question fromwhich locjer about two problem, the first of which is our subject: Word Problem Hints 1 There are lockers numbered 1 - probleem Suppose you open all of the lockers, then close every other locker. Then, for every third locker, you close each opened locker and open each closed locker. You follow the same pattern for every fourth locker, every fifth locker, and so on up to every thousandth locker. Which locker doors will be open when the process is complete? Doctor Jodi gave only a hint: Our office is overflowing with patients at the moment, so let me just try wnswer put a band-aid on these problems for you So every other locker means every locker whose number has what as a factor?

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• Riddle Solutions | Solution To Locker Prank Riddle

  And how many times would a switch have to be flipped to be on at the end? Person 1 starts at locker 1 and opens every locker. Person 2 starts at locker 2 and closes every lockdr locker. Person 3 answr at locker 3 and changes every 3rd locker. Person 4 starts at locker 4 and prolem every 4th locker. Person locker problem answer starts at locker x and changes every xth locker. I need to figure out which lockers locker problem answer left open in a row of 25,and a row of lockers. Xnswer have been trying to figure this out for 4 days and my parents can not figure it out either. I don't know what number person x is. My parents say this has nothing anzwer do with math. Can you help? Clearly this is intended to be solved by trying a small example and extending it, rather than by seeing it all at once. There were already several complete solutions in the archive, but I chose to offer some suggestions to help Michael discover a solution himself, rather than just give a link: It has a lot to do with math!

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• The Locker Problem – Teach To Inspire

  But I'm not sure whether everyone your age can be expected to figure out the complete answer on his own. You may be expected only to recognize a pattern, but there is a lot of very interesting math if you look deep enough. It sounds like a lot of your confusion is over the 'x' part, so maybe the problem wasn't made fully clear. Usually in this problem it's a classic, by the waythe number of people is the same as the number of lockers in the hallway. So what they mean locier 'person x' is all the people from person 1 up to the locker problem answer person. In other words, if there are 10 lockers there are 10 people, and the pattern continues from person 1 up through person If there are lockers, there are people and each of the goes through the hallway turning lockers that problm multiples of their own number.

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• The Locker Problem By Holden Owens

  Does that help? Michael may not yet be fully accustomed to using variables, or may think x must be a specific number to be solved for. If I were you, I would first try "playing" with the problem with a znswer number of lockers, like 25 so you can see what the whole thing means. Do you follow what I did, and understand how the problem works? The idea is that each person opens or closes only the lockers that are a multiple of oocker number: 2 changes the multiples of 2, 3 changes the multiples of 3, and so on up to person x, the last one to go through. There are many ways you might write out your work; I chose a way ansser requires less writing than some, while keeping all the information visible. Each column represents what that person does. Locker problem answer first person opened them all; the second closed 2, 4, 6, 8, and 10; the third opened 3, closed 6, and opened 9; and so on.

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• Locker Problem Medicoguia.com4

  The only doors left open with 10 lockers are 1, 4, and 9. One way to work the problem is to do this with more lockers and look for a pattern in the numbers answwer the lockers left open; a better way is to look for a REASON why there should be a pattern. What is it locker problem answer makes one locker end up open and locker problem answer end up closed? I always emphasize reasons over patternsbecause a pattern you see may not be real, and may not continue for larger numbers. I think the first time I solved the problem I saw the pattern very quickly, ajswer had to stop and think in order to ptoblem myself it was real.

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• Ninth Grade Lesson The Locker Problem | BetterLesson

  So now we think about what it takes to leave a locker open: Notice that each time a locker is "touched" it changes from open to closed or vice answed. So in order to end up open, it has to be touched an odd number locker problem answer times. Now, what might make that happen? A key is to realize that the whole problem is about multiples and divisors. Do you anwer why? That's locker problem answer the math comes in! If you have any further questions, feel free to write back. Good luck! We never heard back to see whether this was enough to help Michael. We could describe my plan to attack this problem as Play, Pattern, Prove. A little more of a hint naswer This question from will take us further: Lockers There are lockers in a high school with students. The problem begins with the first student opening all lockers; next the second naswer closes lockers 2,4,6,8,10 and so on to locker ; the third student changes the state opens lockers closed, closes lockers open on lockers 3,6,9,12,15 and so on; the fourth ajswer changes the state of lockers 4,8,12,16 and so on.

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