public class Permutations : IEnumerable<int[]>
{
    private int _n;
    public Permutations(int n)
    {
        _n = n;
    }

    #region IEnumerable<IEnumerable<int>> Members

    public IEnumerator<int[]> GetEnumerator()
    {
        return new PermutationEnumerator(_n);
    }

    #endregion

    #region IEnumerable Members

    System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator()
    {
        return GetEnumerator();
    }

    #endregion

    private class Pair<F, S>
    {
        public F First { set; get; }
        public S Second { set; get; }

        public Pair(F first, S second)
        {
            First = first;
            Second = second;
        }
    }

    private class PermutationEnumerator : IEnumerator<int[]>
    {
        private int _n;
        public PermutationEnumerator(int n)
        {
            if (n < 0) throw new ArgumentOutOfRangeException("Only non-negative numbers allowed.");

            _n = n;

            Reset();
        }

        #region IEnumerator<IEnumerable<int>> Members

        private int[] _current;
        public int[] Current
        {
            get { return _current; }
        }

        #endregion

        #region IDisposable Members

        public void Dispose()
        {
            _depthPositionMap.Clear();
            _depthPositionMap = null;
            _current = null;
        }

        #endregion

        #region IEnumerator Members

        object System.Collections.IEnumerator.Current
        {
            get { return Current; }
        }

        public bool MoveNext()
        {
            _current = null;

            while (_depthPositionMap.Count > 0 && !GenerateNextPermutation()) ;

            if (_current == null) return false;

            return true;
        }

        public void Reset()
        {
            _current = new int[_n];

            for (int i = 0; i < _n; i++)
            {
                _current[i] = i;
            }

            _depthPositionMap = new SortedList<int, Pair<int, int[]>>();

            _depthPositionMap.Add(0, new Pair<int, int[]>(0, _current));
        }

        #endregion

        private SortedList<int, Pair<int, int[]>> _depthPositionMap = null;

        private bool GenerateNextPermutation()
        {
            int depth = _depthPositionMap.Keys[_depthPositionMap.Count - 1];

            Pair<int, int[]> pair = _depthPositionMap[depth];

            if (depth == pair.Second.Length - 1)
            {
                _current = pair.Second;
                _depthPositionMap.Remove(depth);
                return true;
            }

            if (pair.First == pair.Second.Length)
            {
                _depthPositionMap.Remove(depth);
            }
            else
            {
                int[] elements = pair.Second.ToArray();

                int tmp = elements[pair.First];
                elements[pair.First] = elements[depth];
                elements[depth] = tmp;

                _depthPositionMap.Add(depth + 1, new Pair<int, int[]>(depth + 1, elements));

                pair.First++;
            }

            return false;
        }
    }
}

Now its only a small step to create a generic Permutation-class – and here it is:

public class Permutations<T> : Permutations, IEnumerable<IEnumerable<T>>
{
    T[] _elements;

    public Permutations(IEnumerable<T> collection)
        : base(collection.Count())
    {
        _elements = collection.ToArray();
    }

    #region IEnumerable<IEnumerable<T>> Members

    public new IEnumerator<IEnumerable<T>> GetEnumerator()
    {
        using (IEnumerator<int[]> enumerator = base.GetEnumerator())
        {
            while (enumerator.MoveNext())
            {
                T[] result = new T[enumerator.Current.Length];
                for (int i = 0; i < enumerator.Current.Length; i++)
                {
                    result[enumerator.Current[i]] = _elements[i];
                }
                yield return result;
            }
        }
    }

    #endregion
}

Feel free to comment this approach…

At the beginning my algorithm was just a straight forward Ford-Bellmann after transforming the board and the possible positions of the roboter into a stategraph. I tried to keep the probability in mind while implementing it but after a while i noticed that searching for the best path couldnt get me rid of the problem of not knowing which cards will be next and whether the roboter would be able to follow the path by these cards. But a good friend of mine, Georg Hofmann, gave me a good advice: Monte-Carlo-Simulation. And he also provided the idea of the actual algorithm (i suggest reading the rules of the contest before).

The aim: To get the expected value of needed rounds to reach the target for every field.
Starting values: 1 on every field, 0 for the target field.
Simulation: Draw 8 cards. Calculate for EVERY field (A), which fields can be reached by
these cards and choose the one with the actual lowest expectation value (B). Correct the
expectation value for A as follows: E(A) = 0.9 * E(A) + 0.1 * E(B)
Do the simulation as often as possible to get a good result...

(Of course you have to take care of fields that leads to the dead of the robot – they need some kind of penalty as well as they dont need to be simulated)
After running these little piece of algorithm (very(!) often) the roboter “knows” what to do: Always choose those 5 cards that leads to the field with the lowest expectation value – its statistically best!

I wrote a more detailed article (in german) about this approach in combination with an introduction into C#/Mono for freiesMagazin. The article will be available at the May 2010 edition of freiesMagazin. But this is not the end of the roboters… be prepared

Reminder: Use unique cursor names! (if calling a procedure inside cursor which uses a cursor itself, the cursor names need to be unique)

/// <summary>
/// Reads data from a stream until the end is reached. The
/// data is returned as a byte array. An IOException is
/// thrown if any of the underlying IO calls fail.
/// </summary>
/// <param name="stream">The stream to read data from</param>
/// <param name="initialLength">The initial buffer length</param>
public static byte[] ReadFully (Stream stream, int initialLength)
{
    // If we've been passed an unhelpful initial length, just
    // use 32K.
    if (initialLength < 1)
    {
        initialLength = 32768;
    }

    byte[] buffer = new byte[initialLength];
    int read=0;

    int chunk;
    while ( (chunk = stream.Read(buffer, read, buffer.Length-read)) > 0)
    {
        read += chunk;

        // If we've reached the end of our buffer, check to see if there's
        // any more information
        if (read == buffer.Length)
        {
            int nextByte = stream.ReadByte();

            // End of stream? If so, we're done
            if (nextByte==-1)
            {
                return buffer;
            }

            // Nope. Resize the buffer, put in the byte we've just
            // read, and continue
            byte[] newBuffer = new byte[buffer.Length*2];
            Array.Copy(buffer, newBuffer, buffer.Length);
            newBuffer[read]=(byte)nextByte;
            buffer = newBuffer;
            read++;
        }
    }
    // Buffer is now too big. Shrink it.
    byte[] ret = new byte[read];
    Array.Copy(buffer, ret, read);
    return ret;
}

PS: I dont get paid for any commercial, im just enthusiastic

public static bool In(this object o, IEnumerable c)
{
  foreach(object i in c)
  {
    if(i.Equals(o)) return true;
  }
  return false;
}

I used VirtualBox for a long time – it was great but it was slow! As i decided to switch to Windows 7 i also decided to try an alternativ and what i found was WUBI. And now im happy: Its easier to install than a virtual machine, no need for an extra partition and its fast! The only sad thing: Switching between Windows and Ubuntu needs a computer restart…