2012 AMC 12B Problem 8
Attempt Problem 8 of the 2012 AMC 12B below, then check your answer against the professionally curated solution 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.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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?
Answer: A
Small hint:
Fix Friday as cake, then count the other six days
Big hint:
Each remaining day has choices, anything except the dessert served the following day
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.
Problem 8 in other years
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