Challenge Oct-2024

Cheryl’s Birthday                                                                                  Solutions

“Cheryl’s Birthday” is a well-known logic puzzle from Singapore. The objective is to determine the birthday of a girl named Cheryl using a handful of clues given to her friends Albert and Bernard.

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:

  • May 15, May 16, May 19
  • June 17, June 18
  • July 14, July 16
  • August 14, August 15, August 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know too.
Bernard: At first I didn’t know when Cheryl’s birthday is, but I know now.
Albert: Then I also know when Cheryl’s birthday is.

QUESTION: When is Cheryl’s birthday?

Last month Peter Norvig asked nine LLM chatbots to solve this problem and concluded: “Most of them were familiar with the problem and correctly recalled the answer: July 16. But none of them were able to write a program that finds the solution. They all failed to distinguish the different knowledge states of the different characters over time. At least with respect to this problem, they had no theory of mind.”

Send your solutions to DecisionManagementCommunity@gmail.com.

Solutions: