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))