The Random Native

You come across a fork with two roads ahead and you want to know which to take. Exactly one leads to destination. Three natives $A$, $B$, and $C$ emerge to help. The truth-teller always tells the truth, the liar always a lie, and randomist tosses a fair coin to decide his answer. Too bad you don't know who is who. Can you ask two yes/no questions, each directed to either $A$, $B$, or $C$, to get your answer?

Solution:

The key is to find one who is not random. Ask $A$ if $B$ is more honest than $C$. Note that no matter what, if the answer is yes, then $C$ is not random. Otherwise $B$ is not random. Then, ask this non-randomist: "If I ask you whether the first road takes me to my destination, would you reply yes?" and take the road indicated by the reply.

Box within box

A rectangular box $R$ with dimensions $A$, $B$, and $C$ contains another rectangular box $r$ with dimensions $a$, $b$, and $c$. Both boxes are rigid. Show that $A+B+C\geq a+b+c$. This implies that there is no way of getting cheaper postage by wrapping with another box when postage depends only on the sum of dimensions.

Proof:
It follows directly from two facts.

The first is $AB+AC+BC\geq ab+ac+bc$, or $R$'s surface area is no less than $r$'s. Project each face of $r$ outward onto $R$'s surface. The projections of $6$ faces on $R$ are disjoint and cannot be smaller than the original area.

The second is $A^2+B^2+C^2\geq a^2+b^2+c^2$. Imagine $r$ contains a rigid stick at its diagonal, i.e. with length $\sqrt{a^2+b^2+c^2}$. The stick has to fit in $R$ as well, which can take a stick no longer than $\sqrt{A^2+B^2+C^2}$.

Q.E.D.

What happens in higher dimensional space?