Apparently the Cocoa Beach Hilton - and according to staff - ALL Hiltons are equipped with the World's Dumbest Clock. Mine was 45 minutes slow, not all that unusual. I went to reset it and....
.... no way to set the time! I called the front desk and they said they could send up an "engineer" to fix it for me. I declined the intrusion (memories of the engineer and his assistant arriving in Groucho's stateroom), and googled... lo and behold, found a youtube video on how to set the time on a stupid Hilton clock.
Screw around the back of the top flange - remove it, pop the top off - where the dumb buttons to select "pop" "country" etc are - and underneath are the time set buttons.
Someone really went to a lot of trouble to think up this thing. Someone I hope now fired. But in the future, I know how to fix it...