$n$ .

Calvin thinks of a 5-digit number. He tells you the product of the digits isKnowing only that, there are exactly 200 different numbers which Calvin could have thought of.

Find the sum of all possible values of $n$ .

The answer is 25176.

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<?php

$p = array();

for($i=10000;$i<100000;$i++){

$product = array_product(str_split($i));

if(isset($p[$product])){

$p[$product]++;

} else {

$p[$product] = 1;

}

}

foreach($p as $key=>$val){

if($val!=200){

unset($p[$key]);

}

}

$v = array_keys($p);

echo array_sum($v); //25176

?>