AMC 8 2014 Problem 11
AMC8 2014 年第 11 题
排列与组合★★★☆☆
Jack wants to bike from his house to Jill's house, which is located three blocks east and two blocks north of Jack's house. After biking each block, Jack can continue either east or north, but he needs to avoid a dangerous intersection one block east and one block north of his house. In how many ways can he reach Jill's house by biking a total of five blocks?
Jack 想从他家骑车到 Jill 家去，Jill 家位于 Jack 家向东 3 个街区，向北 2 个街区的位置。当 Jack 骑车经过每个街区后，他可以选择继续向东或者向北，但他必须绕开离他家向东 1 个街区，向北 1 个街区的一个危险的十字路口。那么他经过 5 个街区骑车到 Jill 的家一共有多少种路线？
- A.4
- B.5
- C.6
- D.8
- E.10
正确答案 · Correct Answer
A
解析 · Solution
Solution 1
We can apply complementary counting and count the paths that DO go through the blocked intersection, which is . There are a total of paths, so there are 10-6=4 paths possible. is the correct answer.
We can make a diagram of the roads available to Jack. Then, we can simply list the possible routes. There are 4 possible routes, so our answer is .
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