How to take X amount of questions, that sum up Y amount of difficulty

Question

I have a table

Questions -> Question(string), Difficulty (int, 1-10)

I need to create a method, that as the title mentions, take

Answer 1

Here's one way to do it, using a modified version of the recursive solution found here: Finding all possible combinations of numbers to reach a given sum

First, a public method that will do some quick validation and then call a recursive method to get the results:

/// 

/// Gets lists of numQuestions length of all combinations 
/// of questions whose difficulties add up to sumDifficulty
/// 
/// The list of questions to search
/// The number of questions required
/// The amount that the difficulties should sum to
/// 
public static List> GetQuestions(List questions,
    int numQuestions, int sumDifficulty)
{
    if (questions == null) throw new ArgumentNullException("questions");

    var results = new List>();

    // Fail fast argument validation
    if (numQuestions < 1 || 
        numQuestions > questions.Count ||
        sumDifficulty < numQuestions * Question.MinDifficulty ||
        sumDifficulty > numQuestions * Question.MaxDifficulty)
    {
        return results;
    }

    // If we only need single questions, no need to do any recursion
    if (numQuestions == 1)
    {
        results.AddRange(questions.Where(q => q.Difficulty == sumDifficulty)
            .Select(q => new List {q}));

        return results;
    }

    // We can remove any questions who have a difficulty that's higher
    // than the sumDifficulty minus the number of questions plus one
    var candidateQuestions =
        questions.Where(q => q.Difficulty <= sumDifficulty - numQuestions + 1)
            .ToList();

    if (!candidateQuestions.Any())
    {
        return results;
    }

    GetSumsRecursively(candidateQuestions, sumDifficulty, new List(), 
        numQuestions, results);

    return results;
}

And then the recursive method that does the heavy lifting:

private static void GetSumsRecursively(IReadOnlyList questions, 
    int sumDifficulty, List candidates, int numQuestions, 
    ICollection> results)
{
    int candidateSum = candidates.Sum(x => x.Difficulty);

    if (candidateSum == sumDifficulty && candidates.Count == numQuestions)
    {
        results.Add(candidates);
    }

    if (candidateSum >= sumDifficulty)
        return;

    for (int i = 0; i < questions.Count; i++)
    {
        var remaining = new List();

        for (int j = i + 1; j < questions.Count; j++)
        {
            remaining.Add(questions[j]);
        }

        var filteredCandidates = new List(candidates) {questions[i]};

        GetSumsRecursively(remaining, sumDifficulty, filteredCandidates, 
            numQuestions, results);
    }
}

Here's an example usage:

public static void Main()
{
    const int numberOfQuestions = 3;
    const int sumOfDifficulty = 15;

    // Since I don't have your table, I'm using a list of objects to fake it
    var questions = new List();
    for (int i = 1; i < 11; i++)
    {
        questions.Add(new Question {Difficulty = i % 10 + 1, 
            QuestionString = "Question #" + i});
    }

    var results = GetQuestions(questions, numberOfQuestions, sumOfDifficulty);

    // Write output to console to verify results
    foreach (var result in results)
    {
        Console.WriteLine("{0} = {1}", string.Join(" + ", 
            result.Select(r => r.Difficulty)), sumOfDifficulty);
    }
}

And just so you have everything to make this work, here's my Question class used to fake your table:

internal class Question
{
    public const int MinDifficulty = 1;
    public const int MaxDifficulty = 10;
    private int _difficulty;

    public int Difficulty
    {
        get { return _difficulty; }
        set
        {
            if (value < MinDifficulty) _difficulty = MinDifficulty;
            else if (value > MaxDifficulty) _difficulty = MaxDifficulty;
            else _difficulty = value;
        }
    }

    public string QuestionString { get; set; }
}