MathDB

Let

k

and

n

be positive integers, with

k \geq 2

. In a straight line there are

kn

stones of

k

colours, such that there are

n

stones of each colour. A step consists of exchanging the position of two adjacent stones. Find the smallest positive integer

m

such that it is always possible to achieve, with at most

m

steps, that the

n

stones are together, if: a)

n

is even. b)

n

is odd and

k=3

Problem Statement