# Seven elevators

From Math Puzzle Wiki

## Puzzle

The superintendent of an apartment building tells you that his building has seven elevators. Each elevator stops on at most 6 ﬂoors. He also tells you that you can get to any one ﬂoor from any other ﬂoor without changing elevators (if you take the right elevator). What is the largest number of ﬂoors that the building could have?

## Meta-puzzle

In general, if a building has <m>m</m> elevators which can each visit at most <m>n</m> floors, how many floors could the building have if you must be able to get from any one floor to any other floor by using a single elevator?

## References

Problem Solving by Thomas DeFranco and Charles Vinsonhaler.