MathDB

Let

n\ge 3

be a fixed integer. There are

m\ge n+1

beads on a circular necklace. You wish to paint the beads using

n

colors, such that among any

n+1

consecutive beads every color appears at least once. Find the largest value of

m

for which this task is \emph{not} possible.
Carl Schildkraut, USA

C2