2012 AMC 12B Problem 8
Below is the professionally curated solution for Problem 8 of the 2012 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 12B solutions, or check the answer key.
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Difficulty rating: 1380
8.
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?
Solution:
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 choices each.
The number of menus is
Thus, the correct answer is A.
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