5. Jure drew a regular 9-sided polygon. He wanted to arrange the numbers from 1 to 9 at its vertices such that the sum of the numbers in any three consecutive vertices would not exceed a natural number $n$. For what smallest number $n$ would he have succeeded?

## 53rd Mathematical Competition for High School Students in Slovenia

Selection Competition, April 1, 2009

## Solutions to the Problems

Each problem is worth 7 points. All mathematically and logically correct solutions are equally valid. When evaluating each problem, reasonably consider the provided scoring guide. A contestant should not receive more than 3 points for any problem if the partial solution does not clearly lead to the final solution of the problem.