D_1,D₂, ----are 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 ${\mathrm{D}}_2,{\mathrm{D}}_4,{\mathrm{D}}_6---{\mathrm{D}}_{998},{\mathrm{D}}_{1000}$. Then P₃ changes the status of ${\mathrm{D}}_3,{\mathrm{D}}_6,{\mathrm{D}}_9,{\mathrm{D}}_{12},--$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 ${\mathrm{D}}_4,{\mathrm{D}}_8,{\mathrm{D}}_{12},{\mathrm{D}}_{16}--$ etc (doors having numbers which are multiples of 4). And so on until lastly P₁₀₀₀ changes the status of D₁₀₀₀