Spoilers ahead: for the puzzle and the movies/games
This post assumes you've already solved the puzzle. It reveals all categories and their connections, and discusses plot details, endings, and spoilers for featured movies/games throughout.
The Talented Mr. Ripley (1999) opens with Tom Ripley borrowing a Princeton blazer to impersonate an alumnus at a party. He is not an alumnus. He doesn't know anyone there. He is, by every available measure, completely exposed. He handles it perfectly, and the film is watching someone with no safety net act as though the fall couldn't happen to him. You spend two and a half hours not being sure whether to admire him or understand what he's about to lose.
Movies: Training Day · Glory · Malcolm X · Remember the Titans
Denzel Washington has two modes that are both excellent, and the interesting thing about this group is that all four lie on his moral spectrum, not clustered together.
Glory (1989) is Denzel in his earliest major dramatic register: Robert Gould Shaw's regiment, the 54th Massachusetts Infantry, the Black soldiers fighting for a Union that won't fully commit to their humanity. He won Best Supporting Actor for it. Malcolm X (1992) is three hours of Spike Lee and Denzel building a biographical portrait that doesn't simplify the subject's evolution, the Nation of Islam years, the disillusionment, the assassination. His performance across those three phases is one of the most detailed in American film.
Remember the Titans (2000) is the crowd-pleaser in the group: football, Virginia, 1971, integration. He plays Coach Herman Boone with quiet authority and it works on a mainstream sports movie level while not embarrassing itself.
Training Day (2001) is the one that changes the conversation. Alonzo Harris is a villain, not a complicated hero, not a morally ambiguous lawman, a predatory corrupt cop who manipulates and kills. Denzel won Best Actor for it. Watching him in that role if you've only seen the earlier three is genuinely disorienting, and the disorientation is the point.
Movies: Marriage Story · Jojo Rabbit · Match Point · Vicky Cristina Barcelona
Scarlett Johansson was in four Woody Allen films between 2005 and 2008. Two of them are in this group, which tells you something about their relative quality. Then there's the Taika Waititi, then the Noah Baumbach. The common thread besides Johansson is that all four are movies where desire makes people behave very badly.
Match Point (2005) is the one to press on. London, a social climber, a rich family, an affair with Johansson's Nola that spirals toward a conclusion Woody Allen borrowed from Crime and Punishment without crediting it. It's his best film of that decade and possibly longer. Vicky Cristina Barcelona (2008) is warmer and sunnier and Penélope Cruz won the Oscar for her role in it, which was right. Johansson is good in it. Cruz is transcendent.
Jojo Rabbit (2019) is a WWII satire where Johansson plays a German mother hiding a Jewish girl in her walls, with an imaginary Hitler as Jojo's childish friend. It was nominated for Best Picture. Marriage Story (2019) is Noah Baumbach working out something personal: a couple's divorce told from both sides, slowly, painfully. Johansson and Adam Driver are both doing career-best work and you feel every hour of it.
Movies: Groundhog Day · Edge of Tomorrow · Palm Springs · Source Code
Groundhog Day (1993) wasn't the first time loop story, but it's the one that colonized the concept. Phil Connors is a weatherman who wakes up at 6:00 AM in Punxsutawney, Pennsylvania, every morning, indefinitely. The film never explains why. It also doesn't need to. What it is about is what you'd do with infinite time to practice being a person, which turns out to be harder than it sounds.
Edge of Tomorrow (2014) takes the loop and puts it in a military action context: Tom Cruise dies in an alien invasion, wakes up at the start of the day, repeats. The loop has mechanical stakes. Each iteration is genuine progress. It's a film that understands the game logic of loops better than almost anything else, there's a sequence where the characters communicate through dozens of loops' worth of accumulated knowledge and it's one of the best scenes in any blockbuster of the decade.
Source Code (2011) is thriller-adjacent: a soldier reliving the last eight minutes before a train bombing, trying to identify the bomber. The loop has a fixed duration. Palm Springs (2019) is the romantic comedy take: Andy Samberg and Cristin Milioti are both stuck in their own loops in Palm Springs, which is the right setting for infinite repetition.
All four take the same premise (same day, forever) and reach for completely different emotional registers. The range from horror to comedy to romance to action without any of them fully failing is the argument for the concept.
Movies: Catch Me If You Can · The Talented Mr. Ripley · Matchstick Men · Paper Moon
The con artist film has two flavors. One is the delightful caper: Frank Abagnale Jr. running through airports in a Pan Am uniform, cheerful and untouchable. Catch Me If You Can (2002) is that film. DiCaprio plays Abagnale as charming to the point of unreality, Hanks plays the FBI agent who can't stop smiling while chasing him, and Spielberg makes it feel like a long fond joke at everyone's expense. You leave feeling good about everyone involved, including Abagnale, which is probably the wrong response.
The Talented Mr. Ripley is the other flavor. Tom Ripley lies his way into wealth and sunlight and keeps having to lie to preserve the first lie, and underneath the lying is a person who wants so desperately to be someone else that he eventually forgets the difference. It's a tragedy that wears an Italian vacation on its surface.
Matchstick Men (2003) is the Ridley Scott con film: Nicolas Cage as an OCD grifter, Sam Rockwell as his protégé, a teenage daughter who shows up and disrupts everything. It has one of the cleaner twist executions in the genre. Paper Moon (1973) is Peter Bogdanovich and real-life father and daughter Ryan and Tatum O'Neal selling bibles to widows in Depression-era Kansas. Tatum O'Neal was ten years old when she won Best Supporting Actress for it.
The con artist films are doing something the time loop films aren't: they're about the cost of the performance, not the performance itself. Ripley and Tatum O'Neal's Addie both want something concrete (status, money, belonging) and the elaborate performance is the only access they have to it. The gap between who they are and who they need to be is where all the drama lives.
If repeating the same day appeals to you mechanically rather than cinematically, PixelLinkr has a puzzle category for games that make time loops their entire combat mechanic. Deathloop is in it.