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Solutions from a student (dragged) 1

# Solutions from a student (dragged) 1 - the remaining...

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the remaining passengers will be in their correct seats and certainly the #100’th will also. If he sits in the last seat #100, then certainly the last passenger cannot sit there (in fact he will end up in seat #1). If he sits in any of the 98 seats between seats #1 and #100, say seat k , then all the passengers with seat numbers 2 , 3 , . . . , k - 1 will have empty seats and be able to sit in their respective seats. When the passenger with seat number k enters he will have as possible seating choices seat #1, one of the seats k + 1 , k + 2 , . . . , 99, or seat #100. Thus the options available to this passenger are the same options available to the first passenger. That is if he sits in seat #1 the remaining passengers with seat labels k +1 , k +2 , . . ., 100 can sit in their assigned seats and passenger #100 can sit in his seat, or he can sit in seat #100 in which case the passenger #100 is blocked, or finally he can sit in one of the seats between seat k and seat #99. The only di ff erence is that this k -th passenger has fewer choices for the “middle” seats. This
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