Square digit chains | Project Euler | Problem #92

URL to the problem page: https://projecteuler.net/problem=92


A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before.

For example,

44 → 32 → 13 → 10 → 1 → 1 85 → 89 → 145 → 42 → 20 → 4 → 16 → 37 → 58 → 89

Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. What is most amazing is that EVERY starting number will eventually arrive at 1 or 89.

How many starting numbers below ten million will arrive at 89?

#include <iostream>

using namespace std;

int finddigits(int a) {

    int cnt = 1;

    while (a >= 10) {

        a /= 10;

        cnt++;

    }

    return cnt;

}

int power(int a, int b) {

    int result = 1;

    for (int i = 0; i < b; i++) {

        result *= a;

    }

    return result;

}

int main()

{

    int i, j, number, cnt = 0, digitnumber, digits[8] = { 0 };

    for (i = 1; i < 10000000; i++) {

        number = i;

        while (number != 1) {

            digitnumber = finddigits(number);

            for (j = digitnumber; j > 0; j--) {

                digits[j - 1] = (number % power(10, j)) / (power(10, (j - 1)));

            }

            number = 0;

            for (j = 0; j < digitnumber; j++) {

                number += (power(digits[j], 2));

            }

            if (number == 89) {

                cnt++;

                break;

            }

        }

    }

    cout << "Number of starting numbers that will arrive at 89 below 10.000.000 is  =  " << cnt << endl;

    return 0;

}

CLICK TO SEE THE OUTPUT.