MathDB

Let

k

and

n

be integers with

1\leq k<n

. Alice and Bob play a game with

k

pegs in a line of

n

holes. At the beginning of the game, the pegs occupy the

k

leftmost holes. A legal move consists of moving a single peg to any vacant hole that is further to the right. The players alternate moves, with Alice playing first. The game ends when the pegs are in the

k

rightmost holes, so whoever is next to play cannot move and therefore loses. For what values of

n

and

k

does Alice have a winning strategy?

Problem Statement