Permuted multiples (Euler Problem 52)

Back to overview.

https://projecteuler.net/problem=52

It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.

Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits.

In [56]:
from functools import reduce
from operator import eq

def get_length(n):
    """ Returns the number of digits for n.
        Returns wrong result for n = 0. """
    length = 0
    while n:
        length += 1
        n //= 10
    return length

assert(get_length(100) == 3)

def get_digits(n):
    d = []
    while n:
        d.append(n % 10)
        n //= 10
    return d

assert(get_digits(213) == [3, 1, 2])

def get_digits_count(n):
    digits_count = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
    for d in get_digits(n):
        digits_count[d] += 1
    return digits_count

assert(get_digits_count(1258744) == [0, 1, 1, 0, 2, 1, 0, 1, 1, 0])
In [64]:
def check_if_multiples_contain_same_digits(n, max_multiple=2):
    n_digits_count = get_digits_count(n)
    n_length = get_length(n)
    n_multiple = n * max_multiple
    while n != n_multiple:
        if n_length != get_length(n_multiple) or n_digits_count != get_digits_count(n_multiple):
            return False
        n_multiple -= n
    return True

assert(check_if_multiples_contain_same_digits(125874))
assert(check_if_multiples_contain_same_digits(125875) == False)
In [70]:
for i in range(1, 10000000):
    if check_if_multiples_contain_same_digits(i, 6):
        s = i
        break
In [72]:
print(s)
assert(s == 142857)
142857
In [ ]: