5. At the vertices of a regular 9-gon

(see fig.) place the numbers $2016, 2017, \ldots, 2024$ in such a way that for any three vertices forming an equilateral triangle, one of the numbers is equal to the arithmetic mean of the other two.

![](https://cdn.mathpix.com/cropped/2024_05_06_54c562d050fb6badb826g-04.jpg?height=597&width=614&top_left_y=193&top_left_x=1315)

ANSWER: place the numbers in sequence (other options are possible).
Solution: notice that any three numbers, spaced at equal intervals, work

Lomonosov Moscow State University

## School Olympiad "Conquer Sparrow Hills" in Mathematics

Final Round Tasks for 2015/2016 Academic Year for Grades 5-6