One of the Hardest Math problem I tried!! How to use Pigeonhole Principle to solve this

Описание: [Undergrad, Discrete Mathematics, Combinatorics]
One of the Hardest problem I tried!! It concerns Pigeonhole Principle and Circular sequences. As in many problems, the difficulty lies in deciding the appropriate pigeons and pigeonholes. How to use Pigeonhole Principle to solve this??

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