AMC8 2024
AMC8 2024 · Q13
AMC8 2024 · Q13. It mainly tests Basic counting (rules of product/sum), Casework.
Buzz Bunny is hopping up and down a set of stairs, one step at a time. In how many ways can Buzz Bunny start on the ground, make a sequence of $6$ hops, and end up back on the ground?
(For example, one sequence of hops is up-up-down-down-up-down.)
Buzz Bunny 在楼梯上一步一级地上下跳。在多少种方式下，Buzz Bunny 可以从地面开始，进行 6 次跳跃，并最终回到地面？
（例如，一种跳跃序列是上-上-下-下-上-下。）
(A)
\ 4
\ 4
(B)
\ 5
\ 5
(C)
\ 6
\ 6
(D)
\ 8
\ 8
(E)
\ 12
\ 12
Answer
Correct choice: (B)
正确答案：（B）
Solution
Looking at the answer choices, you see that you can list them out.
Doing this gets you:
$\mathit{UUDDUD}$
$\mathit{UDUDUD}$
$\mathit{UUUDDD}$
$\mathit{UDUUDD}$
$\mathit{UUDUDD}$
Counting all the paths listed above gets you $\boxed{\textbf{(B)} \ 5}$.
查看答案选项，可以直接枚举。
枚举得到：
$\mathit{UUDDUD}$
$\mathit{UDUDUD}$
$\mathit{UUUDDD}$
$\mathit{UDUUDD}$
$\mathit{UUDUDD}$
计数所有路径，得 $\boxed{\textbf{(B)} \ 5}$。
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