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how to cure insomnia in 12 minutes - RTA

📅 May 10, 2026 👤 scraface

May 10, 2026

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📌 Water is drained at 2 cubic meters per minute.

📌 The decay rate is 20%, so 80% remains each year.

📌 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).

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