Mathematics - Permutation & Combination Question with Solution | TestHub

D₁, D₂, ..., D₁₀₀₀ are 1000 doors, and P₁, P₂, ..., P₁₀₀₀ are 1000 persons. Initially, all the doors are closed. P₁ opens all the doors. Then, P₂ closes D₂, D₄, D₆, ..., D₉₉₈, D₁₀₀₀. Then P₃ changes the status of D₃, D₆, D₉, D₁₂, etc. (doors having numbers which are multiples of 3). Changing the status of a door means closing it if it is open and opening it if it is closed. Then P₄ changes the status of D₄, D₈, D₁₂, D₁₆, etc. (doors having numbers which are multiples of 4). This continues until P₁₀₀₀ changes the status of D₁₀₀₀.