.
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 .
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
<?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
?>