MathDB

Let

n

and

k

be positive integers with

1 \leq k \leq n

. A set of cards numbered

1

n

are arranged randomly in a row from left to right. A person alternates between performing the following moves:
[*] The leftmost card in the row is moved

k-1

positions to the right while the cards in positions

2

through

k

are each moved one place to the left. [*] The rightmost card in the row is moved

k-1

positions to the left while the cards in positions

n-k+1

through

n-1

are each moved one place to the right.
Determine the probability that after some number of moves the cards end up in order from

1

n

, left to right.

Problem Statement