A modified Kaprekar number is a positive whole number with a special property. If you square it, then split the number into two integers and sum those integers, you have the same value you started with.
Consider a positive whole number with digits. We square to arrive at a number that is either digits long or digits long. Split the string representation of the square into two parts, and . The right hand part, must be digits long. The left is the remaining substring. Convert those two substrings back to integers, add them and see if you get .
For example, if , then . We split that into two strings and convert them back to integers and . We test , so this is not a modified Kaprekar number. If , still , and . This gives us , the original .
Note: r may have leading zeros.
Here's an explanation from Wikipedia about the ORIGINAL Kaprekar Number (spot the difference!):
In mathematics, a Kaprekar number for a given base is a non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again. For instance, 45 is a Kaprekar number, because 45² = 2025 and 20+25 = 45.
Given two positive integers and where is lower than , write a program to print the modified Kaprekar numbers in the range between and , inclusive.
Complete the kaprekarNumbers function in the editor below. It should print the list of modified Kaprekar numbers in ascending order.
kaprekarNumbers has the following parameter(s):
- p: an integer
- q: an integer
The first line contains the lower integer limit .
The second line contains the upper integer limit .
Note: Your range should be inclusive of the limits.
Output each modified Kaprekar number in the given range, space-separated on a single line. If no modified Kaprekar numbers exist in the given range, print
1 9 45 55 99
, , , , and are the Kaprekar Numbers in the given range.
Solution in Python
def check(i): sq = str(i**2) le = len(str(i)) r = sq[-le:] l = sq[:-le] or '0' return sum(map(int,(l,r)))==i def kaprekarNumbers(p, q): return [i for i in range(p,q+1) if check(i)] p = int(input()) q = int(input()) print(*kaprekarNumbers(p, q) or ["INVALID RANGE"])