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Another difficult grid problem in China TST

Source: China TST 2023 Problem 18

March 29, 2023
matrixcombinatoricssquare grid

Problem Statement

Find the greatest constant λ\lambda such that for any doubly stochastic matrix of order 100, we can pick 150150 entries such that if the other 98509850 entries were replaced by 00, the sum of entries in each row and each column is at least λ\lambda.
Note: A doubly stochastic matrix of order nn is a n×nn\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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