For Pizza Hut's problem on PI day 2016

pizzahut_pi_day.py

## For Pizza Hut's problem on PI day:
## http://blog.pizzahut.com/flavor-news/national-pi-day-math-contest-problems-are-here-2/
##
## I’m thinking of a ten-digit integer whose digits are all distinct. It happens that the
## number formed by the first n of them is divisible by n for each n from 1 to 10.
## What is my number?
##


def dnumber(digits, howmany):
  number = 0
  for i in range(0,howmany):
    number = number * 10 + digits[i]
  return number


def verify(digits):
  for i in range(1,11):
    dn = dnumber(digits, i)
    mod = dn % i
    if mod != 0:
      return False
  return True


def doDigitN(n, digits):
  if n == 10:
    if verify(digits):
      print(digits)
      exit()
    return

  for i in range(0,len(digits)+1):
    newdigits = digits[:]
    newdigits.insert(i, n)
    doDigitN(n+1, newdigits)


doDigitN(0, [])