diff --git a/DIRECTORY.md b/DIRECTORY.md index 3d1bc967e..484484104 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -956,6 +956,8 @@ * [Sol1](project_euler/problem_115/sol1.py) * Problem 116 * [Sol1](project_euler/problem_116/sol1.py) + * Problem 117 + * [Sol1](project_euler/problem_117/sol1.py) * Problem 119 * [Sol1](project_euler/problem_119/sol1.py) * Problem 120 diff --git a/project_euler/problem_117/__init__.py b/project_euler/problem_117/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/project_euler/problem_117/sol1.py b/project_euler/problem_117/sol1.py new file mode 100644 index 000000000..e8214454f --- /dev/null +++ b/project_euler/problem_117/sol1.py @@ -0,0 +1,53 @@ +""" +Project Euler Problem 117: https://projecteuler.net/problem=117 + +Using a combination of grey square tiles and oblong tiles chosen from: +red tiles (measuring two units), green tiles (measuring three units), +and blue tiles (measuring four units), +it is possible to tile a row measuring five units in length +in exactly fifteen different ways. + + |grey|grey|grey|grey|grey| |red,red|grey|grey|grey| + + |grey|red,red|grey|grey| |grey|grey|red,red|grey| + + |grey|grey|grey|red,red| |red,red|red,red|grey| + + |red,red|grey|red,red| |grey|red,red|red,red| + + |green,green,green|grey|grey| |grey|green,green,green|grey| + + |grey|grey|green,green,green| |red,red|green,green,green| + + |green,green,green|red,red| |blue,blue,blue,blue|grey| + + |grey|blue,blue,blue,blue| + +How many ways can a row measuring fifty units in length be tiled? + +NOTE: This is related to Problem 116 (https://projecteuler.net/problem=116). +""" + + +def solution(length: int = 50) -> int: + """ + Returns the number of ways can a row of the given length be tiled + + >>> solution(5) + 15 + """ + + ways_number = [1] * (length + 1) + + for row_length in range(length + 1): + for tile_length in range(2, 5): + for tile_start in range(row_length - tile_length + 1): + ways_number[row_length] += ways_number[ + row_length - tile_start - tile_length + ] + + return ways_number[length] + + +if __name__ == "__main__": + print(f"{solution() = }")