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from typing import List, Tuple def parse_text_and_compute_prime_stats(text: str) -> Tuple[List[int], float]: """Extract all integers from a block of text, filter primes (using a sieve), sort them, and return the sorted list together with the mean of the primes. The function demonstrates text parsing, prim...
**Professor A**: Good afternoon, Professor B. I've been pondering over Euclid's Book XII, particularly the discussions surrounding solid polyhedra within spheres. Have you had a chance to delve into that? **Professor B**: Indeed, I have, Professor A. The corollary on how solid polyhedra in lesser and greater spheres r...
def nearest_prime_distance(points: str, target: float) -> int: """Given a semicolon‑separated list of 2D points in the form "x,y", parse them, compute all pairwise Euclidean distances, round each to the nearest integer, and return the prime number among those rounded distances that is numerically closes...
Question: Consider a rectangular grid of dimensions H x W where each cell is either painted white ('.') or black ('#'). The complexity of the grid is defined as follows: - If all cells are of the same color, the complexity is 0. - Otherwise, divide the grid into two subgrids by a line parallel to one of the sides of t...
Question: Zeke loves to spend time with Penny and likes her. Penny is working on a project involving the transportation of liquefied natural gas (LNG) and is facing a mathematics problem related to counting unique triplets of different numbers. She seeks Zeke's help as she feels he could assist her with the problem. Th...
Question: A rectangular grid with infinitely many rows and columns has a region with N rows and M columns, where each cell contains a card initially facing up. The flipping operation affects the target cell and its adjacent cells (up to eight in total). The presence of specific ions in a solution can alter the flipping...
"Question: You are an adventurer tasked with returning a stolen jewel to the Kingdom of Pal. The jew(...TRUNCATED)
"Question: An integer array $a_1, a_2, \\ldots, a_n$ is being transformed into an array of lowercase(...TRUNCATED)
"Question: Consider a cosmic scenario where n hydrogen atoms are positioned along a linear path on a(...TRUNCATED)
"Modak is a steamed or fried Maharashtrian sweet dumpling made for Ganesh Chaturthi, considered the (...TRUNCATED)
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