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(335) 3

Part of 1992 Tournament Of Towns

Problems(1)

TOT 335 1992 Spring A S3 numbers 1/(i + j - 1) in nxn table

Source:

6/9/2024
The numbers 1i+j−1       (i=1,2,...,n;j=1,2,...,n)\frac{1}{i+j-1} \,\,\,\,\,\,\, (i = 1,2,...,n; j = 1,2,...,n) are written in an nn by nn table: the number 1/(i+j−1)1/(i + j - 1) stands at the intersection of the ii-th row and jj-th column. Chose any nn squares of the table so that no two of them stand in the same row and no two of them stand in the same column. Prove that the sum of the numbers in these nn squares is not less than 11.
(Sergey Ivanov, St Petersburg)
combinatorics