Added Problem 33

project_euler/problem_33/__init__.py

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+

project_euler/problem_33/sol1.py

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+"""
+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))