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A teacher writes six words on a board: “cat dog has max dim tag.” She gives three students, Arshad, Billy and Chloe each a piece of paper with one letter from her favourite word in the list (they each have a different letter from the same word). Then she asks, “Arshad, do you know the word?” Arshad immediately replies "yes". She asks, “Billy, do you know the word?” He thinks for a moment and replies "yes". Then she asks Chloe the same question. She thinks and then replies "yes". What is the teacher's favourite word?
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