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Combinatorics Difficulty 5.0 AIME, harder Find the answer United Kingdom

At a conference, the 2016 participants were registered from P1 to P2016. Each participant from P1 to P2015 shook hands with exactly the same number of participants as the number on their registration form. How many hands did the 2016th participant shake?

(A) $1$ (B) $504$ (C) $672$ (D) $1008$ (E) $2015$

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