/// <summary>
/// https://projecteuler.net/problem=61
/// </summary>
/// <param name="arguments"></param>
/// <returns></returns>
public static Result CyclicalFigurateNumbers(Problem arguments)
{
var numbers = UtilityMath.GetPolygonalNumbers <int>(1009, 9999).ToArray();
var count = numbers.Length;
var types = Enumerable.Range(0, count).ToArray <int>(); // array of polygonal number types used
var setNumberOrder = UtilityString.GeneratePermutations <int>(types); // permutation of the types indicat1ing all combinations of these in a sequence of numbers
var s = UtilityMath.GetNumericalCyclicalSet(setNumberOrder, numbers);
var answer = s.set.Sum().ToString();
var message = string.Format("The sum of the only ordered set of six cyclic 4-digit numbers for which each polygonal type: triangle, square, pentagonal, hexagonal, heptagonal, and octagonal, is represented by a different number in the set is {0}.", answer);
if (Answers[arguments.Id] != answer)
{
message += string.Format(" => INCORRECT ({0})", Answers[arguments.Id]);
}
var r = new Result(arguments.Id, message)
{
Answer = answer
};
return(r);
}
