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Omni-MATH / Since human bodies are 3-dimensional, if one spectator's position is near…

Problem

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problem

Since human bodies are 3-dimensional, if one spectator's position is near another spectator's path of view, then the second one's sight will be blocked by the first one. Suppose that for different i,ji, j, if the circle centered at PiP_{i} with radius 16\frac{1}{6} meter intersects with segment KPjK P_{j}, then AjA_{j} 's sight will be blocked by AiA_{i}, and AjA_{j} could not see the entire show. Which of the following statement is true? (A) If there were 60 spectators, then some of them could not see the entire show; (B) If there were 60 spectators, then it is possible that all spectators could see the entire show, but if there were 800 spectators, then some of them could not see the entire show; (C) If there were 800 spectators, then it is possible that all spectators could see the entire show, but if there were 10000 spectators, then some of them could not see the entire show; (D) If there were 10000 spectators, then it is possible that all spectators could see the entire show.
Plain-text mathematical notation (without MathML)
Since human bodies are 3-dimensional, if one spectator's position is near another spectator's path of view, then the second one's sight will be blocked by the first one. Suppose that for different i,j, if the circle centered at P_(i) with radius (1)/(6) meter intersects with segment KP_(j), then A_(j) 's sight will be blocked by A_(i), and A_(j) could not see the entire show. Which of the following statement is true? (A) If there were 60 spectators, then some of them could not see the entire show; (B) If there were 60 spectators, then it is possible that all spectators could see the entire show, but if there were 800 spectators, then some of them could not see the entire show; (C) If there were 800 spectators, then it is possible that all spectators could see the entire show, but if there were 10000 spectators, then some of them could not see the entire show; (D) If there were 10000 spectators, then it is possible that all spectators could see the entire show.
Original LaTeX notation
Since human bodies are 3-dimensional, if one spectator's position is near another spectator's path of view, then the second one's sight will be blocked by the first one. Suppose that for different $i, j$, if the circle centered at $P_{i}$ with radius $\frac{1}{6}$ meter intersects with segment $K P_{j}$, then $A_{j}$ 's sight will be blocked by $A_{i}$, and $A_{j}$ could not see the entire show. Which of the following statement is true? (A) If there were 60 spectators, then some of them could not see the entire show; (B) If there were 60 spectators, then it is possible that all spectators could see the entire show, but if there were 800 spectators, then some of them could not see the entire show; (C) If there were 800 spectators, then it is possible that all spectators could see the entire show, but if there were 10000 spectators, then some of them could not see the entire show; (D) If there were 10000 spectators, then it is possible that all spectators could see the entire show.

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Source and history

task_id
bd4e6c9f-c3c0-53c2-9b5d-ddea7bbff748
task_key
test--bd4e6c9f-c3c0-53c2-9b5d-ddea7bbff748
task_revision_id
1
config / split
/ test

Official source

initial import