IMO Shortlist 1988 problem 4
Dodao/la:
arhiva2. travnja 2012. An
![n \times n, n \geq 2](/media/m/1/d/8/1d8b2a7d0a46d9fdeaec3205615d4a78.png)
chessboard is numbered by the numbers
![1, 2, \ldots, n^2](/media/m/b/c/3/bc3857cc0271cec8541ccf66689dcd00.png)
(and every number occurs). Prove that there exist two neighbouring (with common edge) squares such that their numbers differ by at least
%V0
An $n \times n, n \geq 2$ chessboard is numbered by the numbers $1, 2, \ldots, n^2$ (and every number occurs). Prove that there exist two neighbouring (with common edge) squares such that their numbers differ by at least $n.$
Izvor: Međunarodna matematička olimpijada, shortlist 1988