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UKMT Junior Kangaroo, 2022

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

I gave both Ria and Sylvie a piece of paper. Each piece of paper had a positive integer written on it. I then told them that the two integers were consecutive. Ria said “I don't know your number”. Then Sylvie said “I don't know your number”. Then Ria said “Ah, I now know your number”. Which of these could be the integer on Ria's piece of paper?

(A) $1$ (B) $2$ (C) $4$ (D) $7$ (E) $11$

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