MathDB

We say that a distribution of students lined upen in collumns is

<span class='latex-italic'>bacana</span>

when there are no two friends in the same column. We know that all contestants in a math olympiad can be arranged in a

<span class='latex-italic'>bacana</span>

configuration with

n

columns, and that this is impossible with

n-1

columns. Show that we can choose competitors

M_1, M_2, \cdots, M_n

in such a way that

M_i

is on the

i

-th column, for each

i = 1, 2, 3, \ldots, n

and

M_i

is a friend of

M_{i+1}

for each

i = 1, 2, \ldots, n - 1

Problem Statement