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[kechettrongtinhyeu]

There are 20 lockers in one hallway of the Quid Pro Quo Academy for Cherubs. In preparation for the beginning of school, the janitor closed all the lockers and put a new coat of paint on the doors which were numbered from 1 – 20. When the 20 students from Mrs. Toliver’s class returned from summer vacation, they decided to celebrate by working off some energy. The first student started at locker one and opened all the locker doors. Student 2 started at locker 2, closed it and every second locker after locker 2. The third student started at locker 3 and changed the state of every 3rd locker including locker 3. (If the locker was open he closed it, if it was closed he opened it) Student #4 started at locker #4 and changed the state of every 4th locker, and so on until all 20 students had passed by all the lockers.
1 after the last student goes by, will locker # 20 be open or closed ? how many time will it have changed state ? expiain your reasoning .
2 which locker changed state the most ? expiain your reasoning
3 which locker changed state the lesst ? expiain your reasoning

4 now there are 200 locker #200 studets to change them .
a . what state will locker # 200 be after all 200 students have passed buy ? how many time will it chanaged state?
b . which locker will be change state the most often ? explain your ressoning
c. which locker will change the state the least ofter ? explain your ressoning