During the Christmas party, five friends sat around a round table in the restaurant with seats labelled 1 to 5. At the New Year party, they sat at the same table again, but each person must have two different neighbors than they had at the Christmas party. In how many ways can they be seated ?
A. 5
B. 10
C. 15
D. 20
E. 30

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Worked solution

1. 2026 AMC 8 官方解析

设5人分别为 $A, B, C, D, E$ .
交换后， $A$ 只能与 $CD$ 相邻

\begin{array}{ccc} & A & \\ C & & D \\ & E \quad B & \end{array} \qquad \begin{array}{ccc} & A & \\ D & & C \\ & B \quad E & \end{array}

考虑可旋转 $. 2 \times 5 = 10$ （种）

Answer

B. 10

AI analysis — may contain mistakes.

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