Nick, the Knight, came upon an ancient castle inhabited by a very strange wizard. The castle has 12 huge doors, each guarded by a fierce dragon and numbered from 1 through 12. The wizard has a strict rule about the use of doors. Knights may enter through any door except number 1. They must take note of the number of the door as they enter, because they are only permitted to leave through a door whose number is a factor or multiple of the number of the entry door. Knights may not exit through the same door they entered. If a knight tries to leave through a wrong door, the dragons are to throw him into the moat with the crocodiles. In how many ways can Nick safely enter and exit this castle?

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A:

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A:

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A:

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