MathDB

A magical castle has

n

identical rooms, each of which contains

k

doors arranged in a line. In room

i, 1 \leq i \leq n - 1

there is one door that will take you to room

i + 1

, and in room

n

there is one door that takes you out of the castle. All other doors take you back to room

1

. When you go through a door and enter a room, you are unable to tell what room you are entering and you are unable to see which doors you have gone through before. You begin by standing in room

1

and know the values of

n

and

k

. Determine for which values of

n

and

k

there exists a strategy that is guaranteed to get you out of the castle and explain the strategy. For such values of

n

and

k

, exhibit such a strategy and prove that it will work.

Problem Statement