2012 AMC 10B Problem 11
Attempt Problem 11 of the 2012 AMC 10B 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 10B solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
11.
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:
Work backward from Friday
Big hint:
Each neighboring day has choices once the next day is fixed
Solution:
We know that there must be cake served on Friday, and as such, on Saturday, we cannot have cake. Therefore, we have choices for Saturday’s menu.
Furthermore, for each of the previous days, we could go backwards and have choices on each day, making the total number of choices
Thus, the correct answer is A .
Problem 11 in other years
- 2000 AMC 10
- 2001 AMC 10
- 2002 AMC 10A
- 2002 AMC 10B
- 2003 AMC 10A
- 2003 AMC 10B
- 2004 AMC 10A
- 2004 AMC 10B
- 2005 AMC 10A
- 2005 AMC 10B
- 2006 AMC 10A
- 2006 AMC 10B
- 2007 AMC 10A
- 2007 AMC 10B
- 2008 AMC 10A
- 2008 AMC 10B
- 2009 AMC 10A
- 2009 AMC 10B
- 2010 AMC 10A
- 2010 AMC 10B
- 2011 AMC 10A
- 2011 AMC 10B
- 2012 AMC 10A
- 2013 AMC 10A
- 2013 AMC 10B
- 2014 AMC 10A
- 2014 AMC 10B
- 2015 AMC 10A
- 2015 AMC 10B
- 2016 AMC 10A
- 2016 AMC 10B
- 2017 AMC 10A
- 2017 AMC 10B
- 2018 AMC 10A
- 2018 AMC 10B
- 2019 AMC 10A
- 2019 AMC 10B
- 2020 AMC 10A
- 2020 AMC 10B
- 2021 AMC 10A Spring
- 2021 AMC 10B Spring
- 2021 AMC 10A Fall
- 2021 AMC 10B Fall
- 2022 AMC 10A
- 2022 AMC 10B
- 2023 AMC 10A
- 2023 AMC 10B
- 2024 AMC 10A
- 2024 AMC 10B
- 2025 AMC 10A
- 2025 AMC 10B