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UKMT Grey Kangaroo, 2018

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

Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line as shown in the diagram. He can make a move either by swapping the position of any two dominoes (without rotating either domino) or by rotating one domino. What is the smallest number of moves he needs to make to arrange all the dominoes correctly?

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $5$

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