Long before meeting Snow White, the seven dwarves lived in seven different mines. There is an underground tunnel connecting any two mines. All tunnels were separate, so you could not start in one tunnel and somehow end up in another. Is it possible to walk through every tunnel exactly once without retracing your path?
There is a queue of \(n\) truth tellers and liars.
The first person says, “more than half of us are liars".
The second person says, “more than a quarter of us are liars".
The third person says, “more than an eighth of us are liars".
...
The \(n\)th person says, “more than \(\frac{1}{2^n}\) of us are liars".
Describe what the number of truth-tellers and liars could be, as well as their placement in the queue. Note that the solutions are not fixed numbers.