Max tried a little reverse psychology on you...clever.
That cat came in, I gave him some of my egg, ham, cheese casserole I'd made for breakfast (seemed the best thing I had around for a cat) and a bowl of water. He ate, drank, clawed on my couch, jumped up on the couch to look at me, let me cuddle him for a few minutes, ran up and down the hallway at a hundred miles an hour for a minute, then stood at the back door yowling to go back out. I put a blanket out for him just in case but he must've gone home.
He has long hair that is well taken care of so I am sure someone owns him but there's no collar. Of course, as they let him outside they may not want the danger of a collar.
I'm pretty sure it's the same cat I saw around last summer. He's so funny, and pretty young.
I don't even know that it's a 'he' I didn't look.