Question 518776: I am trying to find a starting point to help my daughter with the following math problem (right now we are working through it manually with boxes and check marks):
Following recess, the 400 students in a school lined up and entered the school as follows: the first student opened all the 400 lockers in the school. The second student closed all the even numbered lockers. The third student "changed" all the lockers that were numbered with a multiple of 3 by closing those lockers that were opened and opening those lockers that were closed. The fourth student changed all the lockers that were numbered with a multiple of 4 in the same way, and so on. After all 400 students had entered the building in this fashion, which lockers were left open?
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! 1___ o1
2__ o1, c2
3__ o1, c3
4__ o1, c2, o4
5__ o1, c5
6__ o1, c2, o3, c6
7__ o1, c7
8__ o1, c2, o4, c8
9__ o1, c3, o9
10__ o1, c2, 05, c10
11__ o1, c11
12__ o1, c2, o3, c4, o6, c12
13__ o1, c13
14__ o1, c2, o7, c14
15__ o1, c3, o5, c15
16__ o1, c2, o4, c8, o16
25__ o1, c5, o25
36__ o1, c2, o3, c4, o6, c9, o12, c18, o36
I don't know why, but the perfect squares are the ones left open
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