ABCDE Problem

Problem proposed by Kamal Jain:

Solution can be implemented with a simple backtracking, with a bit of pruning during the Check. Not the most efficient solution due to the string operations, but did the trick, and the answer is:

09754,14754,15078,15080,15104,20078,20080,20104

Gemini 2.5 Flash as the clear winner. Code is down below, cheers.

List<string> solutions = new List<string>();

Combination("", 5, ref solutions);

for(int i=0;i<solutions.Count;i++)

    Console.Write("{0}{1}", solutions[i], i < solutions.Count - 1 ? ',' : ' ');

void Combination(string current,

                 int MAX,

                 ref List<string> retVal)

{

    if(current.Length == MAX)

    {

        if(Check(current, MAX, 20320))

            retVal.Add(current);

        return;

    }

    for(int i=0;i<10;i++)

        Combination(current + i.ToString(), MAX, ref retVal);

}

bool Check(string str,

           int MAX,

           int target)

{

    int sum = 0;

    for (int i = 0; i < MAX; i++)

    {

        sum += Int32.Parse(str.Substring(i));

        if (sum > target) return false;

    }

    return sum == target;

}