# The Broken Down Elevator

**Number Theory**Level 3

My building has been undergoing renovation, and the elevator has stopped working as intended.

Every time you push a button for a floor that is lower than the floor for which you are on, the elevator will go down exactly 4 floors. However, if you were on the 2nd, 3rd or 4th floor, the elevator will refuse to work since it can't go down exactly 4 floors.

Every time you push a button for a floor that is higher than the floor for which you are on, the elevator will go up exactly 7 floors. Similarly, if you are near the top, the elevator will refuse to work since it can't go up beyond the building.

Every time you push a button for a floor that is lower than the floor for which you are on, the elevator will go down exactly 4 floors. However, if you were on the 2nd, 3rd or 4th floor, the elevator will refuse to work since it can't go down exactly 4 floors.

Every time you push a button for a floor that is higher than the floor for which you are on, the elevator will go up exactly 7 floors. Similarly, if you are near the top, the elevator will refuse to work since it can't go up beyond the building.

If every single floor can still be reached (from any other floor, albeit tediously) by pushing some sequence of buttons, what is the minimum number of floors of this building?

###### Image credit: Flickr Oregon Department of Transportation

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