The Power of Perfect Squares: Open Lockers Mystery

Which lockers remain open after all students have passed through and changed them?

After all students have changed the lockers, which ones stay open?

Open Lockers Explanation

The lockers that will remain open after all the students have passed through and changed them are the perfect square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

Unlocking the Mystery of Open Lockers

In the locker puzzle scenario, the open lockers are determined by analyzing the number of factors each locker number has. If a locker number has an odd number of factors, it will remain open; if it has an even number of factors, it will be closed.

For example, let's take the locker number 12. Its factors are 1, 2, 3, 4, 6, and 12. Since the factors come in pairs except for perfect squares, the number 12 will end up closed because it has an even number of factors.

On the other hand, perfect square numbers like 9 have an odd number of factors because their square roots are the only factors that don't come in pairs. Therefore, perfect square lockers will remain open after all students have passed through and changed them.

By applying this logic, it is evident that the perfect square numbers between 1 and 100 – 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 – are the lockers that will stay open. These lockers defy the odds and remain unlocked, showcasing the beauty of mathematics in unexpected ways.