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Then the other student came by and open locker 4 and locker 8. Then another student came by and closed locker 5, and opened locker 10. Then the next student came by and closed locker 6. Then another student came by and closed locker 7. Then another student came by and closed locker 8. Then another student came by and opened locker 9. Then the last student came by and closed locker 10. So the remaining lockers open would be 1, 4, and 9. I noticed that these numbers were all squared numbers. 1 is squared number of 1, 4 is the squared number of 2, and 9 is the squared number of 3. I realized this was a pattern, so I didn't even have to use 100 lockers to find out the solution, I just needed to know my squared numbers of each number...
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