MathDB

You are given an odd number

n\ge 3

. For every pair of integers

(i, j)

with

1\le i \le j \le n

there is a domino, with

i

written on one its end and with

j

written on another (there are

\frac{n(n+1)}{2}

domino overall). Amin took this dominos and started to put them in a row so that numbers on the adjacent sides of the dominos are equal. He has put

k

dominos in this way, got bored and went away. After this Anton came to see this

k

dominos, and he realized that he can't put all the remaining dominos in this row by the rules. For which smallest value of

k

is this possible?
Oleksii Masalitin

Problem Statement