1. Imagine you are at a school with 100 lockers, all shut. • • • Suppose the first student goes along and opens every locker. The second student then shuts every other locker, beginning with locker number 2. The third student changes the state of every third locker, beginning with locker number 3. (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 fourth locker, beginning with number 4. Imagine that this continues until the 100 students have followed the pattern with the 100 lockers. At the end, which lockers will be open and which will be closed? Which lockers have been switched the most often? How many lockers, and which ones, were touched exactly five times? Hint: You might initially think about the problem with a small number of lockers and then generalize if possible

1. Imagine you are at a school with 100 lockers, all shut. • • • Suppose the first student goes along and opens every locker. The second student then shuts every other locker, beginning with locker number 2. The third student changes the state of every third locker, beginning with locker number 3. (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 fourth locker, beginning with number 4. Imagine that this continues until the 100 students have followed the pattern with the 100 lockers. At the end, which lockers will be open and which will be closed? Which lockers have been switched the most often? How many lockers, and which ones, were touched exactly five times? Hint: You might initially think about the problem with a small number of lockers and then generalize if possible

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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