Question 172
Find the largest real number $\lambda$ with the following property: for any 100th-order doubly stochastic matrix, it is always possible to select 150 elements from it and change the remaining 9850 elements to zero, such that the resulting matrix has row sums and column sums not less than $\lambda$.
Note: An "$n$th-order doubly stochastic matrix" is an $n \times n$ square matrix in which all elements are non-negative real numbers, and the sum of each row and the sum of each column are both equal to 1.
Note: An "$n$th-order doubly stochastic matrix" is an $n \times n$ square matrix in which all elements are non-negative real numbers, and the sum of each row and the sum of each column are both equal to 1.