Question 13
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 the three vertices is written inside it. Prove that there exist three small triangles such that the sum of the numbers inside them is at least $48$.
