Finding the Longest Chain: A Human Question, a Machine’s Answer, and 156 Trips into The Twilight Zone

In the summer of 2011, during a Twilight Zone marathon, Vance Thompson started wondering about a puzzle. Line up episodes so that each one shares an actor with the next. Never use an episode twice, and never use the same actor as a link twice. How long can the chain get?

It sounds like a question you could settle over a weekend. It took fifteen years.

His first program built chains at random and topped out at sixty episodes. For years, sixty was the record. Then, working with an AI assistant, he went after it again with new programs, a Raspberry Pi running on his dining-room buffet, a friend's Mac tower and finally a brand-new sixteen-core computer. The record kept climbing, and every new high score raised the same question. Was this the longest chain there is, or just the longest one found so far? Along the way he learned that his idle question was a famously hard kind of problem, a cousin of the travelling salesman problem, sitting right on the edge of one of the biggest open questions in computer science.

And then, after months of machines running around the clock, the answer finally came, along with proof that nothing could ever beat it.

Finding the Longest Chain is the story of how that happened, told by someone who is not a mathematician and just wanted to know. It explains the ideas in plain language, from dots and lines to how a problem can be called impossible and still be solved. It is also an honest account of working with an AI on something you care about, including the part where the tool that finished the job had been suggested on the very first day.

The book includes one complete longest chain, episode by episode, the kind of viewing order the author's dad would have suggested, and a few puzzles still waiting for someone to solve them.