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MathNet 2026 — Part 10 Question 119

Math Olympiad Vault · MathNet 2026 — Part 10

Question 119

Cheryl chooses a word in this problem and tells its first letter to Aerith and its last letter to Bob. The following conversation ensues over a series of emails:
Aerith: "I don't know her word, do you?"
Bob: "No, in fact, I don't know if we can ever figure out what her word is without having more information."
Aerith: "Then I do know what it is!"
Bob: "Now I also do."
What is Cheryl's word?