Can large language models solve logic puzzles? There’s one way to find out, which is to ask. That’s what Fernando Perez-Cruz and Hyun Song Shin recently did. (Perez-Cruz is an engineer; Shin is the head of research at the Bank for International Settlements as well as the man who, in the early 1990s, taught me some of the more mathematical pieces of economic theory.)

The puzzle in question is commonly known as the “Cheryl’s birthday puzzle”. Cheryl challenges her friends Albert and Bernard to guess her birthday, and for puzzle-reasons they know it’s one of 10 dates: May 15, 16 or 19; June 17 or 18; July 14 or 16; or August 14, 15 or 17. To speed up the guessing, Cheryl tells Albert her birth month, and tells Bernard the day of the month, but not the month itself.

Albert and Bernard think for a while. Then Albert announces, “I don’t know your birthday, and I know that Bernard doesn’t either.” Bernard replies, “In that case, I now know your birthday.” Albert responds, “Now I know your birthday too.” What is Cheryl’s birthday?* More to the point, what do we learn by asking GPT-4?