Question 8
In this problem, a box is a parallelepiped $P \in \mathbb{R}^3$. We define the size of a box $P$ as $a^s + b^s + c^s$, $a, b, c$ being its dimensions and $s$ a fixed integer.
Find all values of $s$ such that the following statement is true: if a box $P_1$ is inside box $P_0$ then the size of $P_1$ does not exceed size of box $P_0$.
The boxes are allowed to be in any position; in particular, they need not to have its edges parallel to the axes.
Find all values of $s$ such that the following statement is true: if a box $P_1$ is inside box $P_0$ then the size of $P_1$ does not exceed size of box $P_0$.
The boxes are allowed to be in any position; in particular, they need not to have its edges parallel to the axes.