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This problem can be solved using Linear inequality Suppose there are 3 tree initial height speed 2 1 2 3 2 2 there can be 2 possibilities to be trees in zig-zag sequence h1 > h2 < h3 h1 < h2 > h3 Suppose after n unit time , they will be in zig-zag sequence after n unit time height of the tree = speed*time + initial height for first possibility equations will be n+2>3*n+2 -> n<0 invalid condition 3*n+2<2*n+2 -> n<0 invalid condition take intersection of all sol , say it sol1 For second possibility equations will be n+2 < 3*n+2 -> n>0 valid condition 3*n+2 > 2*n + 2 n>0 valid condition take intersection of all sol n>0 ,say it sol2 finally take union of sol1 and sol2 ans will be n>0 ans = [1,INF] You can also refer to my solution