Add Project Euler problem 117 solution 1 (#6872)

Update DIRECTORY.md

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Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

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

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() = }")