Problem

Source: 2023 Iran MO

Tags: combinatorics



4. A positive integer n is given.Find the smallest $k$ such that we can fill a $3*k$ gird with non-negative integers such that: $\newline$ $i$) Sum of the numbers in each column is $n$. $ii$) Each of the numbers $0,1,\dots,n$ appears at least once in each row.