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Omni-MATH / Bob knows that Alice has 2021 secret positive integers x₁,…,x₂₀₂₁ that are pairwise relatively prime. Bob would like to figure out Alice's integers. He is allowed to choose a set …

Problem

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problem

Bob knows that Alice has 2021 secret positive integers x1,…,x2021x_{1}, \ldots, x_{2021} that are pairwise relatively prime. Bob would like to figure out Alice's integers. He is allowed to choose a set S⊆{1,2,…,2021}S \subseteq\{1,2, \ldots, 2021\} and ask her for the product of xix_{i} over i∈Si \in S. Alice must answer each of Bob's queries truthfully, and Bob may use Alice's previous answers to decide his next query. Compute the minimum number of queries Bob needs to guarantee that he can figure out each of Alice's integers.
Plain-text mathematical notation (without MathML)
Bob knows that Alice has 2021 secret positive integers x₁,…,x₂₀₂₁ that are pairwise relatively prime. Bob would like to figure out Alice's integers. He is allowed to choose a set S⊆{1,2,…,2021} and ask her for the product of x_(i) over i∈S. Alice must answer each of Bob's queries truthfully, and Bob may use Alice's previous answers to decide his next query. Compute the minimum number of queries Bob needs to guarantee that he can figure out each of Alice's integers.
Original LaTeX notation
Bob knows that Alice has 2021 secret positive integers $x_{1}, \ldots, x_{2021}$ that are pairwise relatively prime. Bob would like to figure out Alice's integers. He is allowed to choose a set $S \subseteq\{1,2, \ldots, 2021\}$ and ask her for the product of $x_{i}$ over $i \in S$. Alice must answer each of Bob's queries truthfully, and Bob may use Alice's previous answers to decide his next query. Compute the minimum number of queries Bob needs to guarantee that he can figure out each of Alice's integers.

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Source and history

task_id
46c82864-ffce-5297-9215-7969149b6c1e
task_key
test--46c82864-ffce-5297-9215-7969149b6c1e
task_revision_id
1
config / split
/ test

Official source

initial import