Problem:
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 Choices:
A.
B.
C.
D.
E.
Solution:
There are choices for Saturday (anything except cake) and for the same reason choices for Thursday. Similarly there are choices for Wednesday, Tuesday, Monday, and Sunday (anything except what was to be served the following day). Therefore there are possible dessert menus.
If any dessert could be served on Friday, there would be choices for Sunday and for each of the other six days. There would be a total of dessert menus for the week, and each dessert would be served on Friday with equal frequency. Because cake is the dessert for Friday, this total is too large by a factor of . The actual total is .
The problems on this page are the property of the MAA's American Mathematics Competitions