A regular elimination, repeated in a circle, ends up hiding a surprisingly clean structure. The pattern takes a while to appear, but when it does it no longer admits of doubt.
A cyclic elimination
Riddle statement
The positions in a circle are numbered from 1 to \(n\).
First position 2 is eliminated, then 4, then 6, and so on, continuing in a circular fashion between the positions that are still alive, until only one remains.
Which position survives at the end?