Khoisnam figured it out by realizing that lockers toggled an odd number of times would remain open. Only perfect square numbers have an odd number of factors. So, locker numbers that are perfect squares remain open at the end.
Class 8 Mathematics Ganita Prakash A Square and A Cube
Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube NCERT solutions
Khoisnam realized that each locker would be toggled for every factor it has. Most numbers have even factors because they come in pairs. However, perfect squares have one repeated factor, making their count odd. Since an odd number of toggles leaves a locker open, only perfect square locker numbers (like 1, 4, 9…) remain open. This insight helped Khoisnam determine which lockers would stay open without watching the whole process.
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