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INMO 2015 Problem 4

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There are four basket-ball players A,B,C,DA, B, C, D. Initially, the ball is with AA. The ball is always passed from one person to a different person. In how many ways can the ball come back to AA after seven passes? (For example A→C→B→D→A→B→C→AA \rightarrow C \rightarrow B \rightarrow D \rightarrow A \rightarrow B \rightarrow C \rightarrow A and A→D→A→D→C→A→B→AA \rightarrow D \rightarrow A \rightarrow D \rightarrow C \rightarrow A \rightarrow B \rightarrow A are two ways in which the ball can come back to AA after seven passes.)

Dataset text NuminaMath olympiads. Quoted with source.

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