2008 AMC 8 Problem 14
Attempt Problem 14 of the 2008 AMC 8 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 2008 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
14.
Three A’s, three B’s, and three C’s are placed in the nine spaces so that each row and column contain one of each letter. If A is placed in the upper left corner, how many arrangements are possible?
Answer: C
Small hint:
After the top-left A is fixed, decide where the other two A entries can go.
Big hint:
For each A-pattern, the top row can place B and C in two orders.
Solution:
The other two A’s must occupy one square in each of the remaining two rows and columns. There are two possible diagonal patterns for the three A’s.
For either A-pattern, the two remaining positions in the top row can be filled as B,C or C,B, and then the rest of the grid is forced.
So there are arrangements.
Thus, C is the correct answer.
Problem 14 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
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