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Subset without squares

Source: China TST 1993, problem 5

June 27, 2005
algebra unsolvedalgebra

Problem Statement

Let S={(x,y)∣x=1,2,…,1993,y=1,2,3,4}S = \{(x,y) | x = 1, 2, \ldots, 1993, y = 1, 2, 3, 4\}. If T⊂ST \subset S and there aren't any squares in T.T. Find the maximum possible value of ∣T∣.|T|. The squares in T use points in S as vertices.
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