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This is a kind of information deduction problem. Two people are each given incomplete information about some fact (in the original, the month and day of Cheryl's birth) and they make statements which progressively reveal more information to the other. Both the solver and the other character make deductions based on the idea that when one character does not know something, it means there are still two possibilities with all the information that character knows (including half the answer).
MIT Mystery Hunt 2021 Ignorance
MIT Mystery Hunt 2022 Strange Garnets