2005 AMC 8 Problem 3
Attempt Problem 3 of the 2005 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 2005 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
3.
What is the minimum number of small squares that must be shaded so that a line of symmetry lies on the diagonal of square ?
Answer: D
Small hint:
Reflect the shaded squares across diagonal .
Big hint:
Only shaded squares without a matching reflected square need to be paired.
Solution:
For diagonal to be a line of symmetry, every shaded square off the diagonal must have a matching reflected shaded square on the other side of the diagonal.
There are shaded squares whose reflected partners are not shaded, so additional small squares must be shaded.
Thus, D is the correct answer.
Problem 3 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
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
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