8.3. On the table, 28 coins of the same size but possibly different masses are arranged in a triangular shape (see figure). It is known that the total mass of any triplet of coins that touch each other pairwise is 10 g. Find the total mass of all 18 coins on the boundary of the triangle.
Answer: 60 g.

Solution 1: Take a rhombus made of 4 coins. As can be seen from the diagram, the masses of two non-touching coins in it are equal. Considering such rhombi, we get that if we color the coins in 3 colors, as shown in the diagram, then the coins of the same color will have the same mass. Now it is easy to find the sum of the masses of the coins on the boundary: there are 6 coins of each color there, and the sum of the masses of three differently colored coins is 10 g; therefore, the total mass of the coins on the boundary is $6 \cdot 10=60$ g.

![](https://cdn.mathpix.com/cropped/2024_05_06_6c4ade3f29712a9d9297g-1.jpg?height=326&width=314&top_left_y=1993&top_left_x=1585)

Solution 2: All coins except the central one can be divided into 9 triplets, and all internal coins except the central one can be divided into 3 triplets. Therefore, the coins on the boundary weigh as much as 9-3=6 triplets, i.e., 60 g.

Criteria: Only the answer - 0 points.

Rhombi are considered and it is shown that two coins in them have the same mass - 2 points. In addition to this, it is proven that the weights in the entire triangle are as shown in the diagram (coloring is done, but there is no further progress) - another 2 points.