MHB Can someone help me in the right direction with this proof

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A 1001x1001 square table is filled with the numbers 1 to 1001, ensuring each number appears in every row and column. The table is symmetric with respect to one of its diagonals. The discussion revolves around proving that all numbers from 1 to 1001 must appear along this diagonal. The original poster initially sought help but later indicated they solved the problem independently. This highlights the importance of symmetry in mathematical proofs related to structured arrangements.
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A square table of size 1001x1001 is filled with the numbers 1; 2; 3; ... ; 1001 in such a way that in every row
and every column all those numbers appear. If the table is symmetric with respect to one of its diagonals,
prove that in this diagonal all of the numbers 1; 2; 3; ... ; 1001 appear.
 
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