3. At Fishtopia High School, there are 100 seniors preparing for graduation. There are 100 closed...

 

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3. At Fishtopia High School, there are 100 seniors preparing for graduation. There are 100 closed lockers, numbered # 1-100, down a long corridor. As a graduation tradition, all the seniors line up and walk one at a time down the hallway. The first senior changes all the locker positions (so, the first person in line opens all the locker doors). The second senior then changes the position of every other locker (so, since all the lockers are now open, she closes door #2, closes door #4 etc. while not touching door #1 or door # 3, etc.). The third senior then changes the position of every third locker (so, he closes door #3, opens door #6, etc.). This continues until all seniors have had an opportunity to walk down the corridor, only changing the position of the locker doors that correspond with multiples of their position in line. So, for example, senior # 30 will only touch three lockers to change their position (#30, # 60, and # 90) and the last senior only changes the position of locker # 100, while not touching any of the other lockers.[Note: Changing the position of a locker means opening it if it is closed or closing it if it is open.] a. [2 points] How many students touched locker #18? List the numbers of the students who touched locker # 18. Is this locker open or closed at the very end after all 100 seniors have walked down the corridor? b. [2 points] How many students touched locker #25? List the numbers of the students who touched locker # 25. Is this locker open or closed at the very end after all 100 seniors have walked down the corridor? c. [5 points] At the very end, only ten of the lockers will be open. Which lockers will be open at the very end? What special characteristic do these lockers share that resulted in them being the only open lockers? Why do you believe that lockers with this special characteristic will be the only lockers that remain open at the end? Use complete sentences to answer all of the above questions for part c. 3. At Fishtopia High School, there are 100 seniors preparing for graduation. There are 100 closed lockers, numbered # 1-100, down a long corridor. As a graduation tradition, all the seniors line up and walk one at a time down the hallway. The first senior changes all the locker positions (so, the first person in line opens all the locker doors). The second senior then changes the position of every other locker (so, since all the lockers are now open, she closes door #2, closes door #4 etc. while not touching door #1 or door # 3, etc.). The third senior then changes the position of every third locker (so, he closes door #3, opens door #6, etc.). This continues until all seniors have had an opportunity to walk down the corridor, only changing the position of the locker doors that correspond with multiples of their position in line. So, for example, senior # 30 will only touch three lockers to change their position (#30, # 60, and # 90) and the last senior only changes the position of locker # 100, while not touching any of the other lockers.[Note: Changing the position of a locker means opening it if it is closed or closing it if it is open.] a. [2 points] How many students touched locker #18? List the numbers of the students who touched locker # 18. Is this locker open or closed at the very end after all 100 seniors have walked down the corridor? b. [2 points] How many students touched locker #25? List the numbers of the students who touched locker # 25. Is this locker open or closed at the very end after all 100 seniors have walked down the corridor? c. [5 points] At the very end, only ten of the lockers will be open. Which lockers will be open at the very end? What special characteristic do these lockers share that resulted in them being the only open lockers? Why do you believe that lockers with this special characteristic will be the only lockers that remain open at the end? Use complete sentences to answer all of the above questions for part c.

Answer rating: 100% (QA)

a How many students touched locker 18 Factors of 18 1236918 Locker 1 will be touched by 1 student Lo... View the full answer