public void Problem41()
{
var primesUnder1B = new SortedSet <long>(
Sequences
.PrimesUnder(1_000_000)
.ToList()
);
var sum = new BigInteger(0);
for (int i = 1; i <= 9; i++)
{
sum += Functions.Permutations(i, i);
}
Console.WriteLine(sum);
for (int n = 9; n >= 4; n--)
{
// arithmetic series is going to be the sum of the series 1 to n.
// If the sum of the series 1 to n is divisible by 3, all
// permutations of 1 to n will be composites.
if (Series.Arithemtic(n) % 3 != 0)
{
var permutationsOf = Sequences.PermutationsOf(n, 0, 1);
foreach (var permutation in permutationsOf)
{
if (permutation % 2 != 0 && Functions.IsPrime(permutation))
{
Assert.That(permutation, Is.EqualTo(7_652_413));
return;
}
}
}
}
}
public void Problem43()
{
// This is pretty slow.
Func <long, bool> meetsProperty = (permutation) =>
((permutation % 1_000_000_000) / 1_000_000) % 2 == 0 &&
((permutation % 100_000_000) / 100_000) % 3 == 0 &&
((permutation % 10_000_000) / 10_000) % 5 == 0 &&
((permutation % 1_000_000) / 1_000) % 7 == 0 &&
((permutation % 100_000) / 100) % 11 == 0 &&
((permutation % 10_000) / 10) % 13 == 0 &&
((permutation % 1_000)) % 17 == 0;
var sum = Sequences.PermutationsOf(10, 1, 1)
.Where(meetsProperty)
.Sum();
Console.WriteLine(sum);
}
public void Problem32()
{
var permutations = Sequences.PermutationsOf(9, 0, 1)
.ToList();
SortedSet <long> products = new SortedSet <long>();
long sum = 0;
foreach (var permutation in permutations)
{
{
var left = permutation / 10_000_000;
var right = (permutation % 10_000_000) / 10_000;
var product = permutation % 10_000;
if (left * right == product)
{
if (!products.Contains(product))
{
products.Add(product);
}
}
}
{
var left = permutation / 100_000_000;
var right = (permutation % 100_000_000) / 10_000;
var product = permutation % 10_000;
if (left * right == product)
{
if (!products.Contains(product))
{
products.Add(product);
}
}
}
}
Assert.That(products.Sum(), Is.EqualTo(45_228));
}