## Problem of the Day #288: Happy New Year!January 1, 2012

Posted by Alex in : potd , trackback

To celebrate the new year, Albert has decided to open a new hotel. The Hotel Albert consists of 8 rooms.

Two rooms are adjacent if they share an edge. Albert wants to paint each room either red, blue, or green, such a path of rooms with color $X$ can be formed between any two rooms of color $X$. Each color must be used at least once. How many ways are there for Albert to paint his hotel?