Cheryl's Birthday and LLM Theory of Mind Part I

OVERFIT: AI, Machine Learning, and Deep Learning Made Simple

This briefing document analyzes the logic puzzle "Cheryl's Birthday," its sequel, and a related variant. The document explores the origins of the puzzle, presents the puzzle statement and solution, examines a common incorrect solution, and discusses subsequent iterations of the puzzle.

Origins

"Cheryl's Birthday" is a knowledge puzzle that gained widespread attention in 2015 after being posted online by Singaporean television personality Kenneth Kong. The puzzle, authored by Dr. Joseph Yeo Boon Wooi, was initially part of the 2015 Singapore and Asian Schools Math Olympiad (SASMO), intended for high-performing 14-year-old students.

The Puzzle

The puzzle presents a scenario where a girl named Cheryl provides her new friends, Albert and Bernard, with clues to determine her birthday from a list of ten possible dates:

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

Cheryl tells Albert only the month of her birthday and Bernard only the day. The following conversation then takes place:

• 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.

The puzzle asks for Cheryl's birthday.

Solution

The solution is July 16th, derived through a process of elimination and deductive reasoning:

1. Albert's Statement: Albert's statement indicates that he received either July or August, as these months contain multiple possible dates, preventing Bernard from immediately knowing the birthday.
2. Bernard's Statement: Bernard then deduces that Albert must have either July or August. Since Bernard now knows the birthday, he must have been given the day 15, 16, or 17, as these days only appear in one of the possible months.
3. Albert's Deduction: With this new information, Albert can determine the birthday. If Albert had August, he would still be unsure. Therefore, Albert must have July, and the only remaining date in July is the 16th.

Incorrect Solution

A common incorrect solution is August 17th. This arises from neglecting the crucial information conveyed in the latter part of Albert's first statement: "I know that Bernard doesn't know too." This implies that Albert received a month that does not contain unique days like 18 or 19, leading Bernard to eliminate May and June and arrive at a unique date.

Sequels and Variants

Following the viral success of "Cheryl's Birthday," sequels and variations emerged. One sequel, "Cheryl's Age," introduces the ages of Cheryl's two younger brothers and involves deducing Cheryl's age based on the product and sum of their ages.

Another iteration, "Denise's Revenge," involves a new character, Denise, and expands the list of possible birthdays to twenty dates, each with a month, day, and year. The puzzle follows a similar structure of logical deduction based on the characters' statements.

Conclusion

"Cheryl's Birthday" exemplifies the power of logical deduction and careful consideration of seemingly insignificant information within a puzzle. The puzzle and its variants showcase how seemingly simple premises can lead to complex and engaging challenges.