From a041b64f7aaf7dd54f154ba1fb5cd10e3110c1eb Mon Sep 17 00:00:00 2001
From: Maxim Smolskiy <mithridatus@mail.ru>
Date: Mon, 24 Oct 2022 16:29:49 +0300
Subject: [PATCH] feat: add Project Euler problem 073 solution 1 (#6273)

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
---
 DIRECTORY.md                          |  2 ++
 project_euler/problem_073/__init__.py |  0
 project_euler/problem_073/sol1.py     | 46 +++++++++++++++++++++++++++
 3 files changed, 48 insertions(+)
 create mode 100644 project_euler/problem_073/__init__.py
 create mode 100644 project_euler/problem_073/sol1.py

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 10e78a92c..16e6b7ae3 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -839,6 +839,8 @@
   * Problem 072
     * [Sol1](project_euler/problem_072/sol1.py)
     * [Sol2](project_euler/problem_072/sol2.py)
+  * Problem 073
+    * [Sol1](project_euler/problem_073/sol1.py)
   * Problem 074
     * [Sol1](project_euler/problem_074/sol1.py)
     * [Sol2](project_euler/problem_074/sol2.py)
diff --git a/project_euler/problem_073/__init__.py b/project_euler/problem_073/__init__.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/project_euler/problem_073/sol1.py b/project_euler/problem_073/sol1.py
new file mode 100644
index 000000000..2b66b7d87
--- /dev/null
+++ b/project_euler/problem_073/sol1.py
@@ -0,0 +1,46 @@
+"""
+Project Euler Problem 73: https://projecteuler.net/problem=73
+
+Consider the fraction, n/d, where n and d are positive integers.
+If n<d and HCF(n,d)=1, it is called a reduced proper fraction.
+
+If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size,
+we get:
+
+1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3,
+5/7, 3/4, 4/5, 5/6, 6/7, 7/8
+
+It can be seen that there are 3 fractions between 1/3 and 1/2.
+
+How many fractions lie between 1/3 and 1/2 in the sorted set
+of reduced proper fractions for d ≤ 12,000?
+"""
+
+from math import gcd
+
+
+def solution(max_d: int = 12_000) -> int:
+    """
+    Returns number of fractions lie between 1/3 and 1/2 in the sorted set
+    of reduced proper fractions for d ≤ max_d
+
+    >>> solution(4)
+    0
+
+    >>> solution(5)
+    1
+
+    >>> solution(8)
+    3
+    """
+
+    fractions_number = 0
+    for d in range(max_d + 1):
+        for n in range(d // 3 + 1, (d + 1) // 2):
+            if gcd(n, d) == 1:
+                fractions_number += 1
+    return fractions_number
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")