Translative packing of unit squares into equilateral triangles (Q494022)

Let \(t_n\) be the smallest positive number \(t\) such that, for any arbitrarily oriented squares \(S_1,\dots,S_n\) of edge length \(1\) and any equilateral triangle \(T\) of edge length \(t\), there exist translation vectors \(v_1,\dots,v_n \in \mathbb R^2\) such that the translates \(S_i+v_i\), \(i=1,\dots,n\), are packed without overlap in \(T\). It is shown that \(t_1=2.23...\), \(t_2=3.35...\), \(t_4 \leq 4.46...\), \(t_7\leq 6.09...\) and \(t_n < \sqrt{n} \cdot 2.37...\) for \(n \geq 3\).