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Omni-MATH / A 0-1 sequence of length 2^(k) is given. Alice can pick a member from the sequence, and reveal it (its place and its value) to Bob. Find the largest number s for which Bob can alwa…

Problem

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problem

A 0-1 sequence of length 2k2^k is given. Alice can pick a member from the sequence, and reveal it (its place and its value) to Bob. Find the largest number ss for which Bob can always pick ss members of the sequence, and guess all their values correctly. Alice and Bob can discuss a strategy before the game with the aim of maximizing the number of correct guesses of Bob. The only information Bob has is the length of the sequence and the member of the sequence picked by Alice.
Plain-text mathematical notation (without MathML)
A 0-1 sequence of length 2^(k) is given. Alice can pick a member from the sequence, and reveal it (its place and its value) to Bob. Find the largest number s for which Bob can always pick s members of the sequence, and guess all their values correctly.

Alice and Bob can discuss a strategy before the game with the aim of maximizing the number of correct guesses of Bob. The only information Bob has is the length of the sequence and the member of the sequence picked by Alice.
Original LaTeX notation
A 0-1 sequence of length $2^k$ is given. Alice can pick a member from the sequence, and reveal it (its place and its value) to Bob. Find the largest number $s$ for which Bob can always pick $s$ members of the sequence, and guess all their values correctly.

Alice and Bob can discuss a strategy before the game with the aim of maximizing the number of correct guesses of Bob. The only information Bob has is the length of the sequence and the member of the sequence picked by Alice.

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Source and history

task_id
0dcbb724-941b-5f92-9d6d-171c0122c26f
task_key
test--0dcbb724-941b-5f92-9d6d-171c0122c26f
task_revision_id
1
config / split
/ test

Official source

initial import