Question

Jack 想从自己家骑车到 Jill 家，Jill 家位于 Jack 家以东三个街区、以北两个街区。每骑过一个街区后，Jack 可以继续向东或向北，但他需要避开离他家以东一个街区、以北一个街区的危险路口。若他总共骑五个街区到达 Jill 家，有多少种路线？

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?

$4$

$5$

$6$

$8$

$10$

答案：A

知识点：格路补集计数

难度评级：1100

解答：

用 E 表示向东一个街区，N 表示向北一个街区。最短路线使用三个 E 和两个 N。为了避开离 Jack 家以东一格、以北一格的危险路口，前两步必须是 EE 或 NN。

可能路线为 $EEENN$ 、 $EENEN$ 、 $EENNE$ 和 $NNEEE$ ，共 $4$ 条路线。

所以正确答案是 A。

Let E represent traveling one block east and N represent traveling one block north. A shortest route uses three E moves and two N moves. To avoid the dangerous intersection one block east and one block north of Jack's house, the first two moves must be either EE or NN.

The possible routes are $EEENN$ , $EENEN$ , $EENNE$ , and $NNEEE$ , for $4$ routes.

Thus, A is the correct answer.

2014 AMC 8 第 11 题

答案：A

难度评级：1100

解答：

其他年份的第 11 题