IMO 1974 LL SWE36

Origin: SWE

Problem

Consider infinite diagrams D = ... ... ... n20 n21 n22 . . . n10 n11 n12 . . . n00 n01 n02 . . . where all but a finite number of the integers nij, i = 0, 1, 2, . . ., j = 0, 1, 2, . . ., are equal to 0. Three elements of a diagram are called adjacent if there are integers i and j with i \geq0 and j \geq0 such that the three elements are (i) nij, ni,j+1, ni,j+2, or (ii) nij, ni+1,j, ni+2,j, or (iii) ni+2,j, ni+1,j+1, ni,j+2. An elementary operation on a diagram is an operation by which three adjacent elements nij are changed into n′ ij in such a way that |nij −n′ ij| =