function q37()
{
$truncatablePrimes = [];
$expected = 11;
$generator = potentialTruncatablePrimeGenerator();
foreach ($generator as $potentialTruncatablePrime) {
// echo $potentialTruncatablePrime . ' ' . $expected . PHP_EOL;
if (!Number::isTruncatablePrime($potentialTruncatablePrime)) {
continue;
}
--$expected;
$truncatablePrimes[] = $potentialTruncatablePrime;
if ($expected === 0) {
break;
}
}
return array_sum($truncatablePrimes);
}
function q12($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 q44()
{
$pentagonalNumbers = [];
$i = 0;
while (true) {
$pentagonalNumber = Number::pentagonal(++$i);
$pentagonalNumbers[$pentagonalNumber] = $pentagonalNumber;
foreach ($pentagonalNumbers as $firstPentagonalNumber) {
$secondPentagonalNumber = $pentagonalNumber - $firstPentagonalNumber;
if ($firstPentagonalNumber === $secondPentagonalNumber) {
continue;
}
if (!isset($pentagonalNumbers[$secondPentagonalNumber])) {
continue;
}
$difference = $secondPentagonalNumber - $firstPentagonalNumber;
if (isset($pentagonalNumbers[$difference])) {
return $secondPentagonalNumber - $firstPentagonalNumber;
}
}
}
}
function q45($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;
}
}
}
function q23()
{
$limit = 28123;
$lookup = [];
for ($i = 1; $i < $limit; ++$i) {
$isAbundant = Number::getProperDivisorsType($i) === 'abundant';
$lookup[$i] = $isAbundant;
}
$sum = 0;
for ($i = 1; $i < $limit; ++$i) {
$isSumOfAbundant = false;
$maxToTest = (int) ceil($i / 2);
for ($j = 1; $j <= $maxToTest; ++$j) {
if ($lookup[$j] && $lookup[$i - $j]) {
$isSumOfAbundant = true;
break;
}
}
if (!$isSumOfAbundant) {
$sum += $i;
}
}
return $sum;
}
function q43()
{
// Compute the 3 digits values divisible by the given primes
$primes = [2, 3, 5, 7, 11, 13, 17];
$divisibleBy = [];
foreach ($primes as $prime) {
$divisibleBy[$prime] = [];
for ($i = $prime; $i < 1000; $i += $prime) {
// Exclude any multiple of a given prime if it is already not pandigital
if (!Number::isPandigital($i, null, true)) {
continue;
}
$divisibleBy[$prime][] = $i;
}
}
// Generate all the sequences of valid (respecting the constraint specified in the problem) pandigital numbers
$primeSize = count($primes);
$solutionSet = $divisibleBy[$primes[$primeSize - 1]];
for ($i = 1; $i < $primeSize; ++$i) {
$upperPart = $divisibleBy[$primes[$primeSize - $i - 1]];
// dwdxdy
$lowerPart = $solutionSet;
// dxdydz
// Map numbers for efficient matching
$a = [];
foreach ($upperPart as $number) {
$formattedNumber = sprintf('%02d', $number % 100);
$a[$formattedNumber][] = $number;
}
$b = [];
foreach ($lowerPart as $number) {
$formattedNumber = sprintf('%02d', floor($number / pow(10, $i)));
$b[$formattedNumber][] = $number;
}
$intersection = array_intersect_key($a, $b);
$newSolutionSet = [];
foreach ($intersection as $key => $dontCare) {
$upperPart = $a[$key];
$lowerPart = $b[$key];
foreach ($upperPart as $upper) {
$upper = floor($upper / 100);
foreach ($lowerPart as $lower) {
$lower = sprintf('%0' . (2 + $i) . 'd', $lower);
// Since the number has to be pandigital, make sure the digit we're about to add isn't already present
if (strpos($lower, (string) $upper) !== false) {
continue;
}
$value = $upper . $lower;
$newSolutionSet[] = $value;
}
}
}
$solutionSet = $newSolutionSet;
}
// Find the last digit for each solution in the solution set
$finalSolutionSet = [];
foreach ($solutionSet as $solution) {
for ($i = 0; $i < 10; ++$i) {
if (strpos($solution, (string) $i) !== false) {
continue;
}
$finalSolutionSet[] = $i . $solution;
break;
}
}
return array_sum($finalSolutionSet);
}