AMC10 2014 A

AMC10 2014 A · Q4

AMC10 2014 A · Q4. It mainly tests Basic counting (rules of product/sum), Logic puzzles.

Walking down Jane Street, Ralph passed four houses in a row, each painted a different color. He passed the orange house before the red house, and he passed the blue house before the yellow house. The blue house was not next to the yellow house. How many orderings of the colored houses are possible?

Ralph 走在 Jane 街上，经过了四栋一排的房子，每栋涂不同颜色。他经过橙色房子在红色房子之前，经过蓝色房子在黄色房子之前。蓝色房子不挨着黄色房子。有多少种房屋颜色的排序是可能的？

(A) 2 2

(B) 3 3

(D) 5 5

(E) 6 6

Answer

Correct choice: (B)

正确答案：（B）

Solution

If Ralph passed the orange house first, then because the blue and yellow houses are not neighbors, the house color ordering must be orange, blue, red, yellow. If Ralph passed the blue house first, then there are 2 possible placements for the yellow house, and each choice determines the placement of the orange and red houses. These 2 house color orderings are blue, orange, yellow, red, and blue, orange, red, yellow. There are 3 possible orderings for the colored houses.

如果 Ralph 先经过橙色房子，那么因为蓝色和黄色房子不相邻，排序必须是橙色、蓝色、红色、黄色。如果先经过蓝色房子，那么黄色房子有 2 个可能位置，每个位置确定橙色和红色房屋的位置。这 2 种排序是蓝色、橙色、黄色、红色和蓝色、橙色、红色、黄色。共有 3 种可能的房屋颜色排序。

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