Ken's POTW
Five Floor Elevators
The owner of the Party Hotel chain, Happy Harold,
enjoyed a very good business, renting his entire hotel for
group parties (he did especially well during the Spring
vacations of colleges.) Harold also owned an elevator
business and (of course) supplied his hotel with his own
elevators. Harold was a bit frugal, however, and only put six
elevators in his hotel. To make matters worse, his elevator
designers hadn't passed the demonstration phase of their designs
before Harold put them to use and each elevator could stop at
only five floors (the floors weren't necessarily continuous -
the elevators were limited because only that many doors shipped
with the demonstration elevators).
-
Harold's guests found it an intriguing aspect of the hotel that
no more than two elevator rides were needed to reach any floor of the
hotel. What was the maximum number of floors in the hotel?
Can you show a possible configuration for the elevators?
-
Harold's guests said it sometimes took too
long to wait for an elevator on the floors that only had one
elevator stop. Harold built his next hotel such that every
floor had two elevators stop at it, and no two elevators
stopped at the same two floors. Again, no more than two
elevator rides were needed to reach any other floor.
What is the maximum number of floors in this new hotel? Can you
show a possible configuration for the elevators?
-
Although the guests found the multiple elevator rides unique, they
eventually tired of needing to switch. Harold built his next hotel
such that only one elevator ride was necessary to reach any other
floor.
What is the maximum number of floors in this new hotel? Can you
show a possible configuration for the elevators?
Extra Credit: Harold realized that his profits kept getting smaller
as his hotels did, but he never invested in more elevator doors. How
many elevators would he need to build to the height of his first
hotel, but meet the requirements of the last?
Source:
Original.
Solution
Mail to Ken