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    "Let $h$ be the height of the tetrahedron. Then, the volume of the tetrahedron is $\\frac{1}{3} \\cdot 120 \\cdot h = 40h$.<end_working_out><SOLUTION>400</SOLUTION>",
    " \nTo solve this problem, we will use the concept of mass points and the properties of similar triangles. \n\nFirst, let's assign masses to the points based on the given information. Since $M$ is the midpoint of $BC$, we can assign a mass of 1 to both $B$ and $C$. This means that the mass at $M$ is 2 (since $",
    " To solve this problem, we need to find the value of \\( n \\) that minimizes the sum \\( \\sum_{i=1}^{n} f(i) \\) under the given conditions. Let's break down the problem step by step.\n\n1. **Understanding the Constraints:**\n   - \\( f \\) is a non-negative valued function on \\( \\{1, 2"
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