function q12($divisorCount)
{
// We can safely assume that the triangle number which is the sum of $divisorCount numbers
// does not have $divisorCount divisors yet.
$number = $divisorCount;
while (true) {
++$number;
$triangleNumber = Number::triangle($number);
// It should be more likely that an even number be the first number to have more divisors, so lets skip uneven
// numbers
if ($triangleNumber & 1 !== 0) {
continue;
}
$numberOfDivisors = Number::getDivisorsCount($triangleNumber);
if ($numberOfDivisors > $divisorCount) {
return $triangleNumber;
}
}
}
function q45($t, $p, $h)
{
$px = Number::pentagonal($p);
$tx = Number::triangle($t);
while (true) {
$hx = Number::hexagonal(++$h);
$count = 1;
while ($hx >= Number::pentagonal($p + 1)) {
$px = Number::pentagonal(++$p);
}
if ($px === $hx) {
++$count;
}
while ($hx >= Number::triangle($t + 1)) {
$tx = Number::triangle(++$t);
}
if ($tx === $hx) {
++$count;
}
if ($count === 3) {
return $hx;
}
}
}
