I'm doing my homework but i am stuck can you help me? the problem is...... Their are 1000 lockers along a long hall of Westfalls High. The lockers are numbered from 1 to 1000. When the 1000 Westfalls High students return from summer vacation, they decide to celebrate the beginning of the school year by working off some energy. The first student, Student 1, runs down the row of lockers and opens every locker door. Student 2 closes the doors of Lockers 2,4,6,8 and so on. To the end of the line. Student 3 changes the state of the doors of Lockers 3,6,9,12 and so on. To the end of the line (Changes the state means the student opens the locker door if it is closed and closes the door if the door is open.) Student 4 changes the state of the doors of Lockers 4,8,12,16 and so on. Student 5 changes the state of every 5th door. Student 6 changes the state of every 6th door. This pattern continues until all 1000 students have a turn. When all 1000 students have finished, witch locker doors are open, explain your answer make sense..........:shrug:
to all you math wizards! my sons homework
- Thread starter crdshrk007
- Start date
All the doors will be closed except those lockers that are perfect squares. The open lockers will be those that are perfect squares such as 1, 4, 9, 16, 25, 36 and so on. It is a matter of the number of factors that each number has. The lockers are represented by each number and every number that has an even number of factors will be closed while every number (perfect squares) will have an odd number of factors. Those lockers that have an odd number of factors will be manipulated and odd number of times, thus leaving the doors open, those that are manipulated an even number of times have the doors closed. By factors I mean how many numbers it is divisible by. 9 has factors of 1, 3, and 9, three factors. 10 has 1, 2, 5, 10 and even number. open, close, open, close. Get it? I don't know that there is any real formula for this other than factoring.
Hope this helps,
FDC
