In "The Masque of Red Death", what does Prospero's running through all of his rooms and confronting the unknown guest in the seventh room symbolise?
You have asked a very astute question. The answer involves an interpretation of the other symbols in the story to understand what is represented by both the intruder and then by Prospero's movement through the seven rooms. It is clear that this is a richly symbolic tale, and therefore the meaning is closely linked to Poe's use of symbolism.
Let us remember that there are seven rooms, each of a different colour. Seven is a key number that suggests the cycle of life and time passing. For example, we have seven days in a week, and then we have the seven stages of man. Let us also remember that the colour of the seventh room, black, is richly symbolic of death, and likewise we need to recall that it is in this seventh room that the clock (which again symbolises time passing) is housed. Of course, Prospero and his guests have locked themselves away in an attempt to stop the inevitable - to halt the ravages of time of live for eternity. The intruder, who could be said to symbolise death, shows that this is impossible. It is strongly symbolic that as Prospero follows the intruder through the other rooms to the seventh, he is, unknowingly, walking to his death, as he meets the intruder at the final stage of life and dies there.
the rooms represent the stages of life, with blue being birth and black being death. Prospero and the mummer running through all the rooms symbolize one's journey from life to death. He finally catches the intruder while they are in the black room and there is where he dies.