2023 USAMO Problems/Problem 5
Revision as of 21:37, 2 April 2023 by Renrenthehamster (talk | contribs) (Created page with "==Problem== Let <math>n\geq3</math> be an integer. We say that an arrangement of the numbers <math>1</math>, <math>2</math>, <math>\dots</math>, <math>n^2</math> in a <math>n...")
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?