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Home » = \beginpmatrix 2 \\ 5 \\ 11 \endpmatrix - Richter Guitar

= \beginpmatrix 2 \\ 5 \\ 11 \endpmatrix - Richter Guitar

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Since the rectangle is inscribed in the circle, the diagonal of the rectangle is the diameter of the circle.

📌 For the original triangle with side 12 cm:

📌 The diameter of the inscribed circle is equal to the side length of the square, which is 10 cm.

📌 To maximize the total weight, we must assign the $7$ largest available weights to the $7$ features. Since the weights are distinct and none can be reused, we must select $7$ weights from the $10$ and use them in a one-to-one assignment to the features. However, the condition specifies that the highest-weight feature must be assigned the largest value among the $7$, which is automatically satisfied if we assign the $7$ largest weights in decreasing order to the features in increasing order of index.

📌 Thus, the optimal way is to choose $7$ distinct weights from the $10$, and assign them in descending order to the $7$ features — that is, assign the largest weight to feature 1, the second largest to feature 2, and so on, up to the $7$th largest assigned to feature $7$, ensuring the highest feature has the largest weight.

📌 But since the assignment must preserve the maximal total (which is forced by using the $7$ largest weights), and the condition specifies only that the highest feature has the largest weight, we must count the number of permutations of $7$ weights chosen from $10$, where the largest of the selected $7$ is assigned to position $7$ (the highest-indexed feature).

📌 Among these $7$ selected weights, identify the largest one. This weight must be assigned to the feature with the highest index (feature $7$) to satisfy the condition.

📌 The remaining $6$ selected weights (which include $6$ smaller ones) can be assigned to the first $6$ features in any order.

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