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Omni-MATH / Find the greatest constant λ such that for any doubly stochastic matrix of order 100, we can pick 150 entries such that if the other 9850 entries were replaced by 0, the sum of ent…

Problem

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problem

Find the greatest constant

\lambda

such that for any doubly stochastic matrix of order 100, we can pick

150

entries such that if the other

9850

entries were replaced by

0

, the sum of entries in each row and each column is at least

\lambda

. Note: A doubly stochastic matrix of order

n

is a

n\times n

matrix, all entries are nonnegative reals, and the sum of entries in each row and column is equal to 1.

Plain-text mathematical notation (without MathML)

Find the greatest constant λ such that for any doubly stochastic matrix of order 100, we can pick 150 entries such that if the other 9850 entries were replaced by 0, the sum of entries in each row and each column is at least λ.

Note: A doubly stochastic matrix of order n is a n×n matrix, all entries are nonnegative reals, and the sum of entries in each row and column is equal to 1.

Original LaTeX notation

Find the greatest constant $\lambda$ such that for any doubly stochastic matrix of order 100, we can pick $150$ entries such that if the other $9850$ entries were replaced by $0$, the sum of entries in each row and each column is at least $\lambda$.

Note: A doubly stochastic matrix of order $n$ is a $n\times n$ matrix, all entries are nonnegative reals, and the sum of entries in each row and column is equal to 1.

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task_id: 7dedcbcc-3757-5cca-b401-fb90000f6347
task_key: test--7dedcbcc-3757-5cca-b401-fb90000f6347
task_revision_id: 3
config / split: / test

Official source

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