Let's Play Basketball!

Discrete Mathematics Level 2

There are four basketball players, A, B, C and D practicing. Initially, the ball is with A, the ball is passed from one person to a different person. In how many ways can the ball come back to A, after exactly seven passes?

For example: \((A \rightarrow D \rightarrow A \rightarrow D \rightarrow C \rightarrow A \rightarrow B \rightarrow A)\) is a way in which the ball can come back to A after 7 passes .

Hint: This question appeared in the Indian National Maths Olympiad 2015 (INMO 2015).

Image Credit: Wikimedia Reisio

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