Problem 20 · 1999 AMC 8
Hard
Geometry & Measurement
spatial-reasoning
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Answer: B — Figure B.
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Hint 1 of 2
From the front you look along the depth direction, so a tall stack hides any shorter stack behind it. Each column's front height is just its TALLEST stack — the back-to-front numbers collapse to their maximum.
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Hint 2 of 2
Read the map column by column (front and back number in each), keep the bigger one, and you've built the front silhouette.
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Approach: a front view is the max-height projection of each column
- Looking from the front, depth disappears — within a column, the taller stack blocks the view of the shorter one, so the column's height is the maximum of its two numbers.
- Column by column: max(2,1) = 2, max(2,3) = 3, max(4,1) = 4. So the silhouette rises 2, 3, 4 left to right, matching figure B.
- The principle to keep: any single-direction view of a 3-D pile is a projection — collapse the hidden direction by taking the maximum height in each visible column. (Side view would instead take the max across each row.)
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