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Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

How many three-digit numbers are there in which any two adjacent digits differ by 3?

(A) $12$ (B) $14$ (C) $16$ (D) $18$ (E) $20$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.