Question 5
An equilateral triangle with side length $3$ is divided into $9$ equilateral triangles with side length $1$. An integer from $1$ to $10$ is written into every point that is a vertex of a small triangle (colored vertices on the figure), such that all numbers are written exactly once. For every small triangle, the sum of the numbers in its three vertices is written inside it. Prove that at least three of those sums are greater than $11$.
