static void Main()
{
// there are certain bounds on numbers that are a power of another number
// AND also have the same number of digits as said power
// only digits 1 through 9 could even be considered, and as you raise each digit
// to a greater power you eventually hit a breakpoint after which the digit raised
// to a power cannot produce enough digits to match the power. This is what our loop is based
// on.
BigInteger answer = 0;
for (int i = 1; i < 10; ++i)
{
for (int j = 1; j < 22; ++j)
{
BigInteger it = BigInteger.Pow(i, j);
List <BigInteger> digits = Permutator.getDigits(it);
if (digits.Count == j)
{
++answer;
}
}
}
Console.WriteLine("Answer: " + answer);
// Keep the console window open in debug mode.
Console.WriteLine("Press any key to exit.");
Console.ReadKey();
}
static void Main()
{
// We're going to create a permutation dictionary of all
// cubic values up to a certain point. The purpose here is to
// be able to attach a list of all discovered cubic permutations
// to any particular cubic value that when sorted acts as a key
// to this dictionary
BigInteger answer = 0;
Dictionary <BigInteger, List <BigInteger> > cubicDict = new Dictionary <BigInteger, List <BigInteger> >();
int search = 100000;
for (int i = 0; i < search; ++i)
{
// get the cube of the index, convert it to a string,
// sort it, and use the sorted permutation of it's digits
BigInteger it = BigInteger.Pow(i, 3);
List <BigInteger> digits = Permutator.getDigits(it);
digits.Sort();
BigInteger sorted = 0;
for (int j = 0; j < digits.Count; ++j)
{
sorted += BigInteger.Pow(10, j) * digits[j];
}
List <BigInteger> knownPerms;
// we want to enforce the rule that associated permutations
// have the same number of digits
List <BigInteger> sortedDigits = Permutator.getDigits(sorted);
if (sortedDigits.Count == digits.Count)
{
if (cubicDict.TryGetValue(sorted, out knownPerms))
{
knownPerms.Add(it);
if (knownPerms.Count == 5)
{
foreach (BigInteger x in knownPerms)
{
Console.WriteLine(x);
}
answer = i;
break;
}
}
else
{
knownPerms = new List <BigInteger>();
knownPerms.Add(it);
cubicDict.Add(sorted, knownPerms);
}
}
}
Console.WriteLine("Answer: " + answer);
// Keep the console window open in debug mode.
Console.WriteLine("Press any key to exit.");
Console.ReadKey();
}
static int nextDigitFactorial(int x)
{
int ret = 0;
List <int> digits = Permutator.getDigits(x);
Func <int, int> factorial = null;
factorial = y => y <= 1 ? 1 : y *factorial(y - 1);
foreach (int a in digits)
{
ret += factorial(a);
}
return(ret);
}