C# /Linq Yet another Brain Teaser

Answer 1

var count = male.Length + female.Length - male.Intersect( female ).Count();

while (flames.Length > 1)
{
     flames = string.Join( '', flames.Where( (c,i) => i != (count % flames.Length) -1 ).ToArray() );
}

Answer 2

That last calculation part that iterates through the flames-letters and removing one after another can be precalculated.

public static Char GetChar(int diff) {
    var idx = (diff - 1) % 60;
    return "efefmeaelmaafmfaflefefeemsasamfmfallslslesmsasmmaelmlaslslfs"[idx];
}

Some things can be done without linq... unless I totally messed something up.

Answer 3

Step1 and Step2

var firstLookup = firstName.ToLookup(c => c.ToLower());
var secondLookup = secondName.ToLookup(c => c.ToLower());
var allChars = firstLookup.Keys.Union(secondLookup.Keys);
int count =
(
  from c in allChars
  let firstCount = firstLookup[c].Count()
  let secondCount = secondLookup[c].Count()
  select
    firstCount < secondCount ? secondCount - firstCount :
    firstCount - secondCount
).Sum()

Step3 (untested)

List<char> word = "FLAMES".ToList();

while (word.Count > 1)
{
  int wordCount = word.Count;
  int remove = (count-1) % wordCount;
  word =
    word.Select( (c, i) => new {c, i =
      i == remove ? 0 :
      i < remove ? i + wordCount + 1 : 
      i})
    .OrderBy(x => x.i)
    .Select(x => x.c)
    .Skip(1)
    .ToList();
}

char result = word.Single();