Having "1|3|6" in a single column to associate the record with multiple catagories is not the right way to do it. That is why you are having problems now. Even if you can get your "like" query to do what you want, you won't be able to make use of indexes in your query, so your DB will have to scan the whole table.
This seems to be a fairly common mistake for people new to relational databases.
Here is an article on this very site:
http://www.phpbuilder.com/columns/barry20000731.php3
For more info, Google for "database normalization":
http://www.google.com/search?q=database%20normalization
It may seem more complicated, but once you get used to it (and the SQL queries over multiple tables) it's actually easier. It's also faster, because your DB can make use of indexes. Speed-wise it can be a huge difference on large tables (analogy: looking up someone's phone number in a phone book sorted by name (do a "binary search"), verses looking it up in a completely unsorted phone book (go over each entry until you find the right one)).