The Locker Problem

IN this problem we figured out that 31 lockers stayed open and 969 ere closed. The lockers that remained open are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, and all the perfect squares on to 1000. The lockers that remained open had a rule to them that had to do with perfect squares. All the lockers that were open had an odd number of factors due to the fact that a perfect square had the same number twice (Ex: 36= 6x6). The perfect squares are the only numbers that have an odd number of factors due to this repeating digit. If a locker has it’s state changed an odd amount of times, it will be open after every student has touched it.. This depends on how many students touched it, but if locker touched an even number of times, it will end up closed.


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