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Join Mystic Molly as she reveals a spooky tale of a carnival hotel with endless rooms always full, and how the innkeeper accommodated an infinite number of ghosts on Halloween night. Discover the clever solution to fitting spirits in an already packed hotel, avoiding the challenge of infinite rooms. Unravel the enigmatic solution with a twist perfect for the mischievous spirits seeking lodgings on a chilling night. Can you solve the riddle of the ghostly hotel?
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Bell ringer #74 “So the story goes,” Mystic Molly begins, “there is a ghostly hotel in the grounds of a carnival which has an infinite number of rooms. The place is so popular that it is always full. However, should a ghost want a room for the night the innkeeper would just ask the ghost in room 1 to move to room 2, the ghost in 2 to move to 3, and so on for all the rooms. Despite your belief she continues, “On Halloween night, an infinite number of ghosts come to stay.” Can you tell me how he accommodated the spooks?
Answer • You cannot ask the ghost in room 1 to move to room infinity + 1 since there is no such thing. However, you can ask every ghost to move to the room double the number they are in. (i.e 1 moves to 2, 2 moves to 4, 3 moves to 6, etc.) This leaves all the odd numbers free and since there are infinitely many odd numbers, then infinitely many ghosts can be accomodated.
