problem 52

"""
 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.
"""

from collections import defaultdict

def num2digits(num):
  digits = defaultdict(lambda: 0)
  for x in str(num):
    digits[int(x)] += 1
  return digits

def test_num(i):
  digits1 = num2digits(i)
  for j in range(2, 7):
    k = i * j
    digits2 = num2digits(k)
    if digits1 != digits2:
      return False
  return True

def main():
  i = 1
  while not test_num(i):
    i += 1
  return i


print(main())
solution = main()
for i in range(2, 7):
  print(i*solution)