From 80e1c8748a947cd2818aa3d8cdf2d224fd13bda1 Mon Sep 17 00:00:00 2001
From: Charley <56961474+pingings@users.noreply.github.com>
Date: Thu, 31 Oct 2019 12:20:39 +0000
Subject: [PATCH] Added Problem 33 (#1440)

* Create sol1.py

* Create __init__.py

* Update sol1.py

* corrected range

* Update sol1.py
---
 project_euler/problem_33/__init__.py |  1 +
 project_euler/problem_33/sol1.py     | 55 ++++++++++++++++++++++++++++
 2 files changed, 56 insertions(+)
 create mode 100644 project_euler/problem_33/__init__.py
 create mode 100644 project_euler/problem_33/sol1.py

diff --git a/project_euler/problem_33/__init__.py b/project_euler/problem_33/__init__.py
new file mode 100644
index 000000000..8b1378917
--- /dev/null
+++ b/project_euler/problem_33/__init__.py
@@ -0,0 +1 @@
+
diff --git a/project_euler/problem_33/sol1.py b/project_euler/problem_33/sol1.py
new file mode 100644
index 000000000..0992c9693
--- /dev/null
+++ b/project_euler/problem_33/sol1.py
@@ -0,0 +1,55 @@
+"""
+Problem:
+
+The fraction 49/98 is a curious fraction, as an inexperienced
+mathematician in attempting to simplify it may incorrectly believe
+that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s.
+
+We shall consider fractions like, 30/50 = 3/5, to be trivial examples.
+
+There are exactly four non-trivial examples of this type of fraction,
+less than one in value, and containing two digits in the numerator
+and denominator.
+
+If the product of these four fractions is given in its lowest common
+terms, find the value of the denominator.
+"""
+
+
+def isDigitCancelling(num, den):
+    if num != den:
+        if num % 10 == den // 10:
+            if (num // 10) / (den % 10) == num / den:
+                return True
+
+
+def solve(digit_len: int) -> str:
+    """
+    >>> solve(2)
+    '16/64 , 19/95 , 26/65 , 49/98'
+    >>> solve(3)
+    '16/64 , 19/95 , 26/65 , 49/98'
+    >>> solve(4)
+    '16/64 , 19/95 , 26/65 , 49/98'
+    >>> solve(0)
+    ''
+    >>> solve(5)
+    '16/64 , 19/95 , 26/65 , 49/98'
+    """
+    solutions = []
+    den = 11
+    last_digit = int("1" + "0" * digit_len)
+    for num in range(den, last_digit):
+        while den <= 99:
+            if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
+                if isDigitCancelling(num, den):
+                    solutions.append("{}/{}".format(num, den))
+            den += 1
+        num += 1
+        den = 10
+    solutions = " , ".join(solutions)
+    return solutions
+
+
+if __name__ == "__main__":
+    print(solve(2))