public static BigInteger NChooseR(int n, int r)
{
if (r > n)
{
throw new ArgumentException("R cannot be greater than N");
}
return((EulerMath.Factorial(n)) / (EulerMath.Factorial(r) * (EulerMath.Factorial(n - r))));
}
long CalculateFactorialSumOfDigits(int i)
{
BigInteger sum = 0;
foreach (var digit in i.ToString())
{
sum += EulerMath.Factorial(long.Parse(digit.ToString()));
}
return(long.Parse(sum.ToString()));
}
public override long Solve()
{
var stringFactorial = EulerMath.Factorial(number).ToString();
var listOfInts = new List <int>();
foreach (var digit in stringFactorial)
{
listOfInts.Add(Int32.Parse(digit.ToString()));
}
return(listOfInts.Sum());
}
public override long Solve()
{
//starting top left and moving to bottom right can only
//go east (e) or south(s). to travel to the bottom right
//you need to travel exactly N e and N s for a N x N grid.
//Therefore, the total number of routes is all of the permutations
//N e and N s
//N! / (A! * B!) where N = total numbers, with some number repeated A times and another number repeated B times.
// 40! / (20! * 20!) because it would take 20 e routes and 20 s routes.
var easternRoutes = gridSize;
var southernRoutes = gridSize;
return((long)(EulerMath.Factorial(2 * gridSize) / (EulerMath.Factorial(easternRoutes) * EulerMath.Factorial(southernRoutes))));
}
public override long Solve()
{
int N = numbers.Count;
string permutation = "";
int permutationToFind = 1000000 - 1;
for (int i = 1; i < N; i++)
{
int location = (int)(permutationToFind / EulerMath.Factorial(N - i));
permutationToFind = (int)(permutationToFind % EulerMath.Factorial(N - i));
permutation = permutation + numbers[location];
numbers.RemoveAt(location);
if (permutationToFind == 0)
{
break;
}
}
for (int i = numbers.Count - 1; i >= 0; i--)
{
permutation += numbers[i];
}
return(long.Parse(permutation));
}
public Fraction(int numerator, int denominator)
{
this.numerator = numerator;
this.denominator = denominator;
gcf = EulerMath.GreatestCommonFactor(numerator, denominator);
}
