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Problem of the Week 815

A Problem with the Elevators

NEW PRIME! David Slowinski announced the finding of a new largest prime this past week:
21257787 - 1
David's father, Emil, is Professor Emeritus in Chemistry at Macalester and a long time PoW solver.

In an apartment building there are seven elevators, each stopping at no more than six floors. If it is possible to go from any one floor to any other floor without changing elevators, what is the maximum number of floors in the building?

Source: Andy Liu

This week's problem will soon appear in Which Way Did the Bicycle Go?...and other intriguing mathematical mysteries by Joseph Konhauser, Dan Velleman, and Stan Wagon; Dolciani Series, MAA (800-331-1622), September, 1996.

© Copyright 1996 Stan Wagon. Reproduced with permission.

The Math Forum

2 October 1998