The Limber Lambda

Continuing my “Sharpen Up” Series, herewith the next episode.

The problem is to find digits that:

1. For an integer n, divide exactly into n;
2. Also divide exactly into the sum of the digits of n.

For example, 3 divides exactly into 81 and also divides exactly into 8+1 = 9.  Except that the problem gets harder–there’s a requirement to count the digits for a particular base numbering system for which this property holds.  Using base 10, only 3 and 9 satisfy this property.  The problem statement indicates that if a digit appears to be a candidate for all possible numbers with less than 4 digits of the relevant base, then it is deemed true for all numbers.  The trivial cases of 0 and 1 should not be included in the count.

This problem took me 36 minutes to complete–here’s my solution:

using System.Collections.Generic;

// 4:30
// 5:06
// SRM150DIV1_250
public class InterestingDigits
{
    private int[] num = new int[3];

    public int[] digits(int Base)
    {
        List<int> interesting = new List<int>();
        for (int d = 2; d < Base; d++)
        {
            for (int i = 0; i < 3; i++)
                num[i] = 0;
            num[0] = d;
            bool exception = false;
            while (true)
            {
                if (((num[0] + num[1] + num[2]) % d == 0 && 
                     (num[0] + num[1]*Base + num[2]*Base*Base) % d != 0) ||
                    ((num[0] + num[1] + num[2]) % d != 0 && 
                     (num[0] + num[1]*Base + num[2]*Base*Base) % d == 0))
                {
                    exception = true;
                    break;
                }
                if (++num[0] == Base)
                {
                    num[0] = 0;
                    if (++num[1] == Base)
                    {
                        num[1] = 0;
                        if (++num[2] == Base)
                        {
                            break;
                        }
                    }
                }
            }
            if (!exception)
            {
                interesting.Add(d);
            }
        }
        return interesting.ToArray();
    }
}