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MMLU-Pro / 10465 / Let X be uniformly distributed over {1,2,…,256}. We ask random…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Let XX be uniformly distributed over {1,2,…,256}\{1, 2, \ldots, 256\}. We ask random questions: Is X∈S1X\in S_1? Is X∈S2X\in S_2? ... until only one integer remains. All 22562^256 subsets of {1,2,…,256}\{1, 2, \ldots, 256\} are equally likely. How many deterministic questions are needed to determine XX?
Plain-text mathematical notation (without MathML)
Let X be uniformly distributed over {1,2,…,256}. We ask random questions: Is X∈S₁? Is X∈S₂? ... until only one integer remains. All 2²56 subsets of {1,2,…,256} are equally likely. How many deterministic questions are needed to determine X?
Original LaTeX notation
Let $X$ be uniformly distributed over $\{1, 2, \ldots, 256\}$. We ask random questions: Is $X\in S_1$? Is $X\in S_2$? ... until only one integer remains. All $2^256$ subsets of $\{1, 2, \ldots, 256\}$ are equally likely. How many deterministic questions are needed to determine $X$?

category

computer science

options

  1. 1024
  2. 64
  3. 1
  4. 512
  5. 8
  6. 16
  7. 4
  8. 32
  9. 256
  10. 128

src

theoremQA-EECS

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Source and history

upstream_id / Original problem ID
10465
task_id
fd0cc77c-594d-5cc2-9188-be82e5b7c648
task_key
default--test--10465
task_revision_id
1
config / split
default / test

Official source

initial import