45.php

<!-- 
Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
Triangle	 	Tn=n(n+1)/2	 	1, 3, 6, 10, 15, ...
Pentagonal	 	Pn=n(3n−1)/2	 	1, 5, 12, 22, 35, ...
Hexagonal	 	Hn=n(2n−1)	 	1, 6, 15, 28, 45, ...
It can be verified that T285 = P165 = H143 = 40755.
Find the next triangle number that is also pentagonal and hexagonal.
 -->
<?php $startTime = microtime(true);

function getHexagonal($input){
	return $input*((2*$input)-1);
}
function isTriangle($input){
	$number = (sqrt((8*$input)+1)-1)/2;
	if (floor($number) == $number)
	{
		return true;
	}
	return false;
}
function isPentagonal($input){
	$number = (sqrt((24*$input)+1)+1)/6;
	if (floor($number) == $number)
	{
		return true;
	}
	return false;
}
//also built these functions, will probably be useful in future problems
// function getTriangle($input){
// 	return ($input*($input+1))/2;
// }
// function getPentagonal($input){
// 	return ($input*((3*$input)-1))/2;
// }
// function isHexagonal($input){
// 	$number = (sqrt((8*$input)+1)+1)/4;
// 	if (floor($number) == $number)
// 	{
// 		return true;
// 	}
// 	return false;
// }
$result = 0;
$n = 144;//start with 143+1
while ($result==0) {
	$num = getHexagonal($n);
	if (isPentagonal($num) && isTriangle($num)) {
		$result = $num;
	}
	$n++;
}

$answer = $result;
$endTime = microtime(true);
echo "Answer: ",$answer,"\nTime: ",($endTime - $startTime),"\n";
// Answer: 1533776805
// Time: 0.022s