Did it for me. Found all files without an, at least one character, extension. AND is implicit in the newer Alfresco versions.
filter cm:content was a good idea, missed it in the first shot (boaah... so many nodes without extension )
I used the slingshot search via an angularjs SPA, so the count of documents without extension was present in milliseconds. A feature of Solr, which gives you the count of matches directly in the result header.