Problem:
The letters , , and are entered into a table according to the pattern shown below. How many s, s, and s will appear in the completed table?
Answer Choices:
A. , ,
B. , ,
C. , ,
D. , ,
E. , ,
Solution:
Since , the bottom letters in each column will occur one more time than the third letter. This means that the third letter in each column will occur times, whereas the other will appear times. Using the same analysis, we can see that and appear in the third row times, whereas only appears times. Therefore, in columns, and appear times, for a total of times. They also appear times in columns, adding appearances to the total. This gives us a total of appearances for and . will therefore appear times.
Thus, is the correct answer.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions