Problem #71 MEDIUM
The Colour-Blind Painter
Google Adobe Combinatorics Graph Theory
Problem Statement
A painter is given a 1×n strip of tiles. She must colour each tile either red or blue such that no two adjacent tiles share the same colour. How many distinct valid colourings exist for a strip of n tiles? Now suppose a third colour — green — is also allowed, but the same adjacency rule applies: no two neighbouring tiles can share the same colour. How many valid colourings exist for n tiles with 3 colours?
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