Problem

TxO Math Bowl 2024 - Individuals A - Problem 15

A set \mathcal{S} has 2024 elements. Suppose that the number of tuples of sets (S_1, S_2, \dots, S_{15}) that satisfy the following conditions is k:

  • Each set S_i is a subset of \mathcal{S}.
  • For every even i, S_i contains both S_{i-1} and S_{i+1}.

Find the remainder when k is divided by 100.


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Problem Tags: Counting and probability Set theory

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