project_euler.problem_073.sol1

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?

Functions

solution(→ int)

Returns number of fractions lie between 1/3 and 1/2 in the sorted set

Module Contents

project_euler.problem_073.sol1.solution(max_d: int = 12000) → 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