Suppose there are 1000 doors namely D1,D2,D3,...,D1000 and there are 1000 persons namely P1,P2,P3,...,P1000. First P1 opens all the doors. Then P2 closes all even numbered doors. P3 changes every third door (i.e., he closes D3, opens D6 and so on). Similarly Pm changes every mth door. Finally P1000 opens D1000 if it were closed, and closes it if it were open.
At the end how many doors remain open

• 31 doors are open.
  
  All perfect squared numbered doors Like 1,4,9,16,.......961 are open.
• 12 years agoHelpfull: Yes(4) No(0)