Question

一位甜点师从星期日开始，为一周中的每天准备甜点。每天的甜点是蛋糕、派、冰淇淋或布丁。同一种甜点不能连续两天供应。因为有人过生日，星期五必须供应蛋糕。这一周有多少种不同的甜点菜单？

A dessert chef prepares the dessert for every day of a week starting with Sunday. The dessert each day is either cake, pie, ice cream, or pudding. The same dessert may not be served two days in a row. There must be cake on Friday because of a birthday. How many different dessert menus for the week are possible?

$729$

$972$

$1024$

$2187$

$2304$

答案：A

知识点：乘法原理有限制的排列

难度评级：1380

解答：

星期五固定为蛋糕。从星期五向两边计数。

另外六天（星期六，然后是星期四、星期三、星期二、星期一、星期日）都可以选择除已经确定的相邻那天甜点之外的任意一种甜点，因此各有 $3$ 种选择。

菜单数为 $3^6=729$ 。

因此正确答案是 A。

Friday is fixed as cake. Work outward from Friday.

Each of the other six days (Saturday, then Thursday, Wednesday, Tuesday, Monday, Sunday) can be any dessert except the one served on the neighboring already-chosen day, giving $3$ choices each.

The number of menus is $3^6=729.$

Thus, the correct answer is A.

2012 AMC 12B 第 8 题

答案：A

难度评级：1380

解答：

其他年份的第 8 题