2000 AMC 8 Problem 12
Attempt Problem 12 of the 2000 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 2000 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
12.
A block wall feet long and feet high will be constructed using blocks that are foot high and either feet long or foot long (no blocks may be cut). The vertical joins in the blocks must be staggered as shown, and the wall must be even on the ends. What is the smallest number of blocks needed to build this wall?
Answer: D
Small hint:
Start with all -foot blocks
Big hint:
Only every other row needs an extra block to stagger joins
Solution:
The total number of rows in the wall is with each row being foot high.
To use the minimum number of bricks, rows and will have the same pattern as the bottom row in the picture, which requires bricks to construct.
Rows and will have the same pattern as the upper row in the picture, which has -foot bricks in the middle and one -foot brick on each end, for a total of bricks.
When you add up rows of bricks and rows of bricks, you get a total of bricks.
Thus, D is the correct answer.
Problem 12 in other years
- 1985 AMC 8
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