MathDB

Let

k,n,r

be positive integers and

r<n

. Quirin owns

kn+r

black and

kn+r

white socks. He want to clean his cloths closet such there does not exist

2n

consecutive socks

n

of which black and the other

n

white. Prove that he can clean his closet in the desired manner if and only if

r\geq k

and

n>k+r

Problem Statement