Subset union

Problem #257

$X$ is a set of size $202020$ . Let $S_1, S_2 \dots S_{100}$ be subsets of $X$ , such that:

For any distinct indices

$a, b, c$ , the union of

$S_a, S_b, S_c$ is not equal to

$X$ .

For any distinct indices

$a, b, c, d$ , the union of

$S_a, S_b, S_c, S_d$ is equal to

$X$ .

Find the maximum value of $|S_1| + |S_2|\dots + |S_{100}|$ .

Contributed by Sawarnik Kaushal

Solved by 38 users

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