2019 AMC 12A 第 3 题

Question

一个盒子里有

28

个红球、

20

个绿球、

19

个黄球、

13

个蓝球、

11

个白球和

9

个黑球。从盒子里不放回地取球，至少要取出多少个球才能保证至少有

15

个球颜色相同？

A box contains

28

red balls,

20

green balls,

19

yellow balls,

13

blue balls,

11

white balls, and

9

black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least

15

balls of a single color will be drawn?

75

76

79

84

91

答案：B

知识点：抽屉原理

难度评级：1020

小提示：

考虑最坏情况：尽可能多取球，但始终不达到同一种颜色

15

个

Consider the worst case: draw as many as possible without ever reaching

15

of one color

大提示：

对每种至少有

14

个的颜色各取

14

个，并取完数量较少的颜色

Take

14

of each color that has at least

14,

and all balls of the smaller colors

解答：

最坏情况下，我们取红、绿、黄各

14

个，再取完所有蓝球

(13),

白球

(11),

和黑球

(9),

仍没有任何一种颜色达到

15

个。

这共有

14 + 14 + 14 + 13 + 11 + 9 = 75

个球。

再取下一个球就一定会凑成某种颜色的

15

个，所以需要

76

个球。

所以正确答案是 B。

In the worst case, we draw

14

each of red, green, and yellow, plus all of the blue

(13),

white

(11),

and black

(9),

without reaching

15

of any color.

That is

14 + 14 + 14 + 13 + 11 + 9 = 75

balls.

The next ball must complete a set of

15,

so

76

balls are needed.

Thus, the correct answer is B.

2019 AMC 12A 第 3 题

答案：B

难度评级：1020

小提示：

大提示：

解答：

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