Following a suggestion of W.M. Schmidt and L. Summerer, we construct a proper 3-system (P 1,P 2,P 3) with the property ̄φ 3 = 1. In fact, our method generalizes to provide n-systems with ̄φn = 1, for arbitrary n ≥ 3. We visualize our constructions with graphics. We further present explicit examples of numbers ξ 1,...,ξn −1 that induce the n-systems in question.