Problem

Source:

Tags: combinatorics unsolved, combinatorics



Suppose there are $n$ boxes in a row and place $n$ balls in them one in each. The balls are colored red, blue or green. In how many ways can we place the balls subject to the condition that any box $B$ has at least one adjacent box having a ball of the same color as the ball in $B$? [Assume that balls in each color are available abundantly.]