The Locker problem
The pattern is 1 open, 2 shut, 1 open, 4 shut, 1 open, 6 shut, etc. The numbers that have a perfect square are the numbers that are open. A perfect square has an odd number of factors so; the square roots are touched odd numbers of times. When the 17th person comes along it doesn’t touch any number before 17 so, all those numbers before 17 stay in the same state. An an example for factors is this one: 16: 16, 1, 2, 8, & 4. 18: 1, 18, 2, 9, 3, 6. There are 5 numbers for 16 so it goes open, closed, open, close, and open. For 18: open, close, open, close, open, and close. One of the factors of 16 is 4; its 4x4 but you put 4 only once. There are 31 square numbers from 1-1000. So, there are 31 lockers opened and 969 lockers closed.
The pattern is 1 open, 2 shut, 1 open, 4 shut, 1 open, 6 shut, etc. The numbers that have a perfect square are the numbers that are open. A perfect square has an odd number of factors so; the square roots are touched odd numbers of times. When the 17th person comes along it doesn’t touch any number before 17 so, all those numbers before 17 stay in the same state. An an example for factors is this one: 16: 16, 1, 2, 8, & 4. 18: 1, 18, 2, 9, 3, 6. There are 5 numbers for 16 so it goes open, closed, open, close, and open. For 18: open, close, open, close, open, and close. One of the factors of 16 is 4; its 4x4 but you put 4 only once. There are 31 square numbers from 1-1000. So, there are 31 lockers opened and 969 lockers closed.
the chart -->
is the state the locker are in
& the patern
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