inspira.php

<?php

$numbers = str_split("0123456789");
$solutions = inspira($numbers);

foreach ($solutions as $solution) {
	echo $solution . "\n";
}

echo "Found " . count($solutions) . " solutions\n";


function inspira($numbers, $reducedNumbers = array()) {
    $return = array();
    foreach($numbers as $key => $value) {
        $copy = $reducedNumbers;
        $copy[$key] = $value;
        $tmp = array_diff_key($numbers, $copy);
        if (count($tmp) == 0) {
	        $a = (array_shift($copy) . array_shift($copy) . array_shift($copy));
			$b = (array_shift($copy) . array_shift($copy));
			$c = (array_shift($copy) . array_shift($copy) . array_shift($copy));
			$d = (array_shift($copy) . array_shift($copy));
			if ($a * $b == $c * $d) {
				$index = [(int)$a, (int)$b, (int)$c, (int)$d];
				sort($index);
				$return[implode("_", $index)] = "$a * $b - $c * $d = 0";
			}
        } else {
            $return = array_merge($return, inspira($tmp, $copy));
        }
    }
    return $return;
}