public static long Problem43()
{
/*
* The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.
*
* Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note the following:
*
* d2d3d4=406 is divisible by 2
* d3d4d5=063 is divisible by 3
* d4d5d6=635 is divisible by 5
* d5d6d7=357 is divisible by 7
* d6d7d8=572 is divisible by 11
* d7d8d9=728 is divisible by 13
* d8d9d10=289 is divisible by 17
* Find the sum of all 0 to 9 pandigital numbers with this property.
*/
List <string> numbers = Formulas.PandigitalNumbers(0, 9);
List <long> primes = Formulas.PrimeSieve(20);
long result = 0L;
foreach (string str in numbers)
{
bool buf = true;
for (int i = 1; i <= 7; i++)
{
if (Int64.Parse(String.Concat(String.Concat(str[i], str[i + 1]), str[i + 2])) % primes.ElementAt(i - 1) != 0)
{
buf = false;
}
}
if (buf)
{
result += Int64.Parse(str);
}
}
return(result);
}
public static long Problem49()
{
/*
* The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.
* There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.
* What 12-digit number do you form by concatenating the three terms in this sequence?
*/
List <long> primes = Formulas.PrimeSieve(10000);
List <long> numbers = new List <long>();
List <string> results = new List <string>();
int limit = 10000;
foreach (long n in primes)
{
if (n > 1000)
{
numbers.Add(n);
}
}
for (int i = 0; i < numbers.Count(); i++)
{
for (int j = i + 1; j < numbers.Count; j++)
{
long k = numbers[j] + (numbers[j] - numbers[i]);
if (k < limit && numbers.Contains(k))
{
if (Formulas.IsPermutation((int)numbers[i], (int)numbers[j]) && Formulas.IsPermutation((int)numbers[i], (int)k))
{
if (numbers[i] != 1487)
{
results.Add(String.Concat(numbers[i], numbers[j], k));
}
}
}
}
}
return(Int64.Parse(results[0]));
}
public static long Problem24()
{
/*
* A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:
*
* 012 021 102 120 201 210
*
* What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?
*/
List <string> permutations = new List <string>();
string seed = "0123456789";
Formulas.Permute(seed.ToArray(), 0, 9, permutations);
permutations.Sort();
Console.Out.WriteLine("Found " + permutations.Count() + " permutations");
return(Int64.Parse(permutations[999999]));
}
public static long Problem50()
{
long result = 0L;
int resCount = 0;
long limit = 1000000;
List <long> primes = Formulas.PrimeSieve(limit);
for (int i = primes.Count - 1; i >= 0; i--)
{
/*
* The prime 41, can be written as the sum of six consecutive primes:
*
* 41 = 2 + 3 + 5 + 7 + 11 + 13
* This is the longest sum of consecutive primes that adds to a prime below one-hundred.
*
* The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953.
*
* Which prime, below one-million, can be written as the sum of the most consecutive primes?
*/
long l = 0L;
long j = i;
int c = 0;
while (l < limit && j >= 0)
{
l += primes.ElementAt((int)j);
j--;
c++;
if (c > resCount && Formulas.isPrime(l))
{
resCount = c;
result = l;
}
}
}
return(result);
}
public static long Problem41()
{
/*
* We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.
* What is the largest n-digit pandigital prime that exists?
*/
List <long> primes = Formulas.PrimeSieve(10000000);
long result = 0L;
foreach (long p in primes)
{
if (Formulas.isPandigital(p))
{
result = p;
}
}
return(result);
}
public static long Problem36()
{
/*
* The decimal number, 585 = 1001001001 (binary), is palindromic in both bases.
* Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.
* (Please note that the palindromic number, in either base, may not include leading zeros.)
*/
long result = 0L;
for (int i = 0; i < 1000000; i++)
{
string b = Convert.ToString(i, 2);
if (Formulas.IsPalindrome(b) && Formulas.IsPalindrome(Convert.ToString(i)))
{
Console.Out.WriteLine(i + " -> " + b);
result += i;
}
}
return(result);
}
public static long Problem206()
{
//Smarter bruteforce (387 420 489) possibilities
Stopwatch sw = new Stopwatch();
sw.Start();
decimal start = Math.Floor(Formulas.Sqrt(10203040506070809.0m) / 10.0m);
decimal end = Math.Floor(Formulas.Sqrt(19293949596979899.0m) / 10.0m);
long dr = -1L;
RegexUtil.setExpression("1.2.3.4.5.6.7.8.9");
for (long i = (long)start; i < (long)end; i++)
{
dr = i * 10 + 3;
if (RegexUtil.isMatching((dr * dr).ToString()))
{
break;
}
dr = i * 10 + 7;
if (RegexUtil.isMatching((dr * dr).ToString()))
{
break;
}
if (i % 10000 == 0)
{
Console.WriteLine(((i - start) / (end - start) * 100.0m) + "%");
}
}
sw.Stop();
return((long)(dr * 10.0m));
}
public static long Problem52()
{
/*
* It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.
* Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits
*/
int x = 0;
bool ok = true;
do
{
x++;
ok = true;
for (int i = 2; i < 7; i++)
{
if (!Formulas.IsPermutation(x * i, x))
{
ok = false;
}
}
} while (!ok);
return(x);
}
public static long Problem38()
{
return(Formulas.LargestPandigital(1, 9));
}