2011 AMC 12A 第 2 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

2.

55 枚硬币按图示平放在桌上。按从上到下的顺序,这些硬币应怎样排列?

There are 55 coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?

(C,A,E,D,B)(C, A, E, D, B)

(C,A,D,E,B)(C, A, D, E, B)

(C,D,E,A,B)(C, D, E, A, B)

(C,E,A,D,B)(C, E, A, D, B)

(C,E,D,A,B)(C, E, D, A, B)

答案:E
知识点:逻辑推理
难度评级:840
解答:

硬币 CC 画成一个完整且没有中断的圆,所以没有东西盖住它,它在最上面。

继续观察其余重叠处,未被遮住的弧线显示每枚硬币在下一枚硬币上方:CC 盖住 EEEE 盖住 DDDD 盖住 BBAA 盖住 BB,同时在其他硬币下方。因此从上到下的顺序是 (C,E,D,A,B)(C, E, D, A, B)

因此,正确答案是 E

Coin CC is drawn as a complete, unbroken circle, so nothing covers it and it lies on top.

Reading the remaining overlaps, each coin's uncovered arc shows it sits above the next: CC covers E,E, EE covers D,D, DD covers B,B, and AA covers BB while lying under the others. This gives the top-to-bottom order (C,E,D,A,B).(C, E, D, A, B).

Thus, the correct answer is E.

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