data/problems/116.yml
---
:id: 116
:name: Red, green or blue tiles
:url: https://projecteuler.net/problem=116
:content: "A row of five black square tiles is to have a number of its tiles replaced
with coloured oblong tiles chosen from red (length two), green (length three), or
blue (length four).\n\nIf red tiles are chosen there are exactly seven ways this
can be done.\n\n| \n\n|  | 
|  |  |\n\n | \n\n|
 |  |  |  |\n\n | \n\n|  |  | 
|  |\n\n | \n\n| 
|  |  |  |\n\n |\n| \n\n|  |  |  |\n\n | \n\n|  |  | 
|\n\n | \n\n|  | 
|  |\n\n | |\n\nIf green tiles are chosen
there are three ways.\n\n| \n\n|  |  |  |\n\n | \n\n|  |  | 
|\n\n | \n\n|  | 
|  |\n\n | |\n\nAnd if blue tiles are chosen
there are two ways.\n\n| \n\n|  |  |\n\n | \n\n|  |  |\n\n |\n\nAssuming that colours cannot be mixed there are 7 + 3
+ 2 = 12 ways of replacing the black tiles in a row measuring five units in length.\n\nHow
many different ways can the black tiles in a row measuring fifty units in length
be replaced if colours cannot be mixed and at least one coloured tile must be used?\n\nNOTE:
This is related to [Problem 117](problem=117).\n\n"