Question 140
Consider a regular polygon with $360$ vertices labeled clockwise from $1$ to $360$. Starting at vertex $1$, count clockwise and remove the $359$th vertex. Continue counting from the next vertex, and remove the subsequent $358$th vertex. Repeat this process, removing the subsequent $357$th vertex, and so on, until only one vertex remains. Determine the label of the last remaining vertex. Note that once a vertex is removed, it is no longer counted.
(Batbayasgalan Balkhuu)
(Batbayasgalan Balkhuu)