There just happens to be 3,333 at the school . All the lockers are numbered from
ID: 3197296 • Letter: T
Question
There just happens to be 3,333 at the school . All the lockers are numbered from 1 to 3,333 and are closed. Student #1, Johan, will go and reverse (open) every 1 locker. The #2 student, Joe, will go and reverse (close) every 2nd locker, i.e. lockers 2, 4, 6, etc. The #3 student, Dan, will reverse (sometimes close and sometimes open) every 3rd locker. The #4 student, Tony, will do the same to every 4th locker. This will continue until student #3,333 (Joe - he had trouble getting out of his car) will get to just visit the last locker and reverse it. Which lockers are open at the end of Feldman’s grand plan? Make a chart. Do a smaller case like 30 or 40 lockers. Find the pattern. There just happens to be 3,333 at the school . All the lockers are numbered from 1 to 3,333 and are closed. Student #1, Johan, will go and reverse (open) every 1 locker. The #2 student, Joe, will go and reverse (close) every 2nd locker, i.e. lockers 2, 4, 6, etc. The #3 student, Dan, will reverse (sometimes close and sometimes open) every 3rd locker. The #4 student, Tony, will do the same to every 4th locker. This will continue until student #3,333 (Joe - he had trouble getting out of his car) will get to just visit the last locker and reverse it. Which lockers are open at the end of Feldman’s grand plan? Make a chart. Do a smaller case like 30 or 40 lockers. Find the pattern.Explanation / Answer
I think all the square numbers will be open, all others will be closed because the squares are the only numbers with an odd number of distinct factors..
Therefore the pattern is 1,4,9,16,25,36.........
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