This may seem too obvious, but the problem is that $result is not a valid MySQL resource. So why is that? Since your other queries work, we have to assume your connection is good. So the almost sure candidate is your query. Something is wrong with your query. Try changing your code to this:

[PHP]
if (!$result = mysql_query($query)) {
die(mysql_error());
}
$num_result = mysql_num_rows($result);
[/PHP]
This should print an error message that indicates what is wrong with the query.

Refer to http://us3.php.net/manual/en/function.mysql-error.php

Another thing I like to do when I'm having trouble with a query is run it directly against the database rather than in a PHP page. Do you have access to run the query directly against the database? For example, command line or phpMyAdmin? These tools give you nice feedback telling you what's wrong.