2 problems

Let $q\geq 2$ be an integer, let $n\geq 3-2^{1-q}$, and for points $x_1,\ldots,x_n\in\mathbb{R}^q$ let $S(x_1,\ldots,x_n)$ be the smallest $(q-1)$-dimensional sphere enclosing them…

Let $q\geq 2$ be an integer. For points $x_1,\ldots,x_n\in\mathbb{R}^q$, let $S(x_1,\ldots,x_n)$ be the smallest $(q-1)$-dimensional sphere enclosing them, and let…