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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