¶ 2008 AMC8 Problem 14
Problem:
Three s, three s and three s are placed in the nine spaces so that each row and column contain one of each letter. If is placed in the upper left corner, how many arrangements are possible?
.jpg)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are only two possible spaces for the in row and only two possible spaces for the in row . Once these are placed, the entries in the remaining spaces are determined.
The four arrangements are:
The s can be placed either
In each case, the letter next to the top can be or . At that point the rest of the grid is completely determined. So there are possible arrangements.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions