AMC 8 1986 Problem 9

AMC8 1986 年第 9 题

基本计数原理★★☆☆☆

Using only the paths and the directions shown, how many different routes are there from

\text{M}

\text{N}

只使用所示路径和方向，从

\text{M}

到

\text{N}

有多少条不同路线？

正确答案 · Correct Answer

解析 · Solution

Solution 1

After one step, the possible routes are

M \rightarrow A

and

M \rightarrow B

After two steps, the possible routes are

M \rightarrow A \rightarrow D

M \rightarrow A \rightarrow C

M \rightarrow B \rightarrow A

M \rightarrow B \rightarrow C

, and

M \rightarrow B \rightarrow N

(complete).

After three steps, the possible routes are

M \rightarrow A \rightarrow D \rightarrow C

M \rightarrow A \rightarrow C \rightarrow N

(complete),

M \rightarrow B \rightarrow A \rightarrow D

M \rightarrow B \rightarrow A \rightarrow C

, and

M \rightarrow B \rightarrow C \rightarrow N

(complete).

After four steps, the possible routes are

M \rightarrow A \rightarrow D \rightarrow C \rightarrow N

(complete),

M \rightarrow B \rightarrow A \rightarrow D \rightarrow C

, and

M \rightarrow B \rightarrow A \rightarrow C \rightarrow N

(complete).

After five steps, the only possible route is

M \rightarrow A \rightarrow B \rightarrow C \rightarrow D \rightarrow N

(complete).

Therefore, there 6 paths from

M

N

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