The locker problem was about the amount of lockers that would be opened up out of a thousand of them. Let's say that the first kid opens up every locker. Then the next kid, the second kid, would change the lockers with factors that have two in it. Thirty one of the one thousand lockers are open. All of the lockers are perfect squares, mainly because they have to open and close an odd number of times. This is because they have to open and close an odd number of times. If they were to open an odd number of times, it would most likely go open, closed, open. In the diagram below, it should show the lockers that are open through fifty.
Total lockers open in 50: 7
All lockers open
1x1=1 19x19=361
2x2=4 20x20=400
3x3=9 21x21=441
4x4=16 22x22=484
5x5=25 23x23=529
6x6=36 24x24=576
7x7=49 25x25=625
8x8=64 26x26=676
9x9=81 27x27=729
10x10=100 28x28=784
11x11=121 29x29=841
12x12=144 30x30=900
13x13=169 31x31=961
14x14=196
15x15=225
16x16=256
17x17=289
18x18=324
All lockers open
1x1=1 19x19=361
2x2=4 20x20=400
3x3=9 21x21=441
4x4=16 22x22=484
5x5=25 23x23=529
6x6=36 24x24=576
7x7=49 25x25=625
8x8=64 26x26=676
9x9=81 27x27=729
10x10=100 28x28=784
11x11=121 29x29=841
12x12=144 30x30=900
13x13=169 31x31=961
14x14=196
15x15=225
16x16=256
17x17=289
18x18=324
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