2023 USAMO Problems/Problem 5
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Problem
Let 
be an integer. We say that an arrangement of the numbers 
, 
, 
, 
in a 
table is row-valid if the numbers in each row can be permuted to form an arithmetic progression, and column-valid if the numbers in each column can be permuted to form an arithmetic progression. For what values of 
is it possible to transform any row-valid arrangement into a column-valid arrangement by permuting the numbers in each row?
