Keep Inserting and Break Filters

Computer Science Level pending

A bloom filter is equipped with 2 16 2^{16} bits and 2 7 2^7 hash functions.

What is the expected number of distinct elements one needs to insert into the filter so that every subsequent query returns a positive, i.e, no matter what the query is, the bloom filter (often incorrectly) claims that the element exists?


The answer is 5973.8.

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