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UKMT Grey Kangaroo, 2024

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

How many eight-digit numbers can be written using only the digits 1, 2 and 3 so that the difference between any two adjacent digits is 1?

(A) $16$ (B) $20$ (C) $24$ (D) $28$ (E) $32$

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