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Inmo 2015

Source: inmo 2015 #4

February 1, 2015
analytic geometrypigeonhole principlecombinatoricsrecursion

Problem Statement

There are four basketball 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 <spanclass=′latex−bold′>seven</span><span class='latex-bold'>seven</span> moves? (for example A→C→B→D→A→B→C→AA\rightarrow C\rightarrow B\rightarrow D\rightarrow A\rightarrow B\rightarrow C\rightarrow A, or A→D→A→D→C→A→B→A)A\rightarrow D\rightarrow A\rightarrow D\rightarrow C\rightarrow A\rightarrow B\rightarrow A).
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