One picture a day, cut the same way for everyone in the world, with a table of who finished it fastest. A new puzzle every midnight UTC. Free to play, and the times are verified by the server rather than taken on trust.
The picture and the cut are derived from the date itself, so every player provably gets the identical puzzle without anything having to be sent between them. It is 100 pieces, the same count every day, so one day's time means something against another's.
Your clock starts on the server the moment you open the puzzle, not in your browser, and a finish is only recorded once the server has read your board back and confirmed every piece is genuinely in place. One entry per person per day. This matters more than it sounds: a leaderboard where the browser reports its own time is a leaderboard of who is willing to edit their own score.
Only to appear on the table. Anyone can play the daily puzzle without signing in — a time just needs a name that somebody owns, or the board would be worthless within a day. Browse other puzzles if you would rather pick your own picture.