Hi, here’s your problem today. This problem was recently asked by Facebook:

Kaprekar’s Constant is the number 6174. This number is special because it has the property where for any 4-digit number that has 2 or more unique digits, if you repeatedly apply a certain function it always reaches the number 6174.

This certain function is as follows:

• Order the number in ascending form and descending form to create 2 numbers.
• Pad the descending number with zeros until it is 4 digits in length.
• Subtract the ascending number from the descending number.
• Repeat.

Given a number n, find the number of times the function needs to be applied to reach Kaprekar’s constant. Here’s some starter code:

KAPREKAR_CONSTANT = 6174

def num_kaprekar_iterations(n):
  # Fill this in.

print num_kaprekar_iterations(123)
# 3
# Explanation:
#  3210 - 123 = 3087
#  8730 - 0378 = 8352
#  8532 - 2358 = 6174 (3 iterations)