2004 AMC 8 Problem 15
Attempt Problem 15 of the 2004 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 2004 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
15.
Thirteen shaded and six unshaded hexagonal tiles were used to create the figure below. If a new figure is created by attaching a border of unshaded tiles with the same size and shape as the others, what will be the difference between the total number of unshaded tiles and the total number of shaded tiles in the new figure?
Answer: C
Small hint:
The original figure has one center tile, a ring of and a ring of
Big hint:
The next hexagonal border has tiles.
Solution:
The original figure has shaded tiles and unshaded tiles.
The new border is the next hexagonal ring around the figure, which has unshaded tiles.
The new figure has unshaded tiles and shaded tiles, so the difference is
Thus, C is the correct answer.
Problem 15 in other years
- 1985 AMC 8
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