2003 AMC 12A Problem 13
Attempt Problem 13 of the 2003 AMC 12A 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 2003 AMC 12A solutions, or check the answer key.
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13.
The polygon enclosed by the solid lines in the figure consists of congruent squares joined edge-to-edge. One more congruent square is attached to an edge at one of the nine positions indicated. How many of the nine resulting polygons can be folded to form a cube with one face missing?
Answer: E
Solution:
A cube missing one face has faces, so the fifth square must fold onto a face not already occupied by the four-square piece. Tracing the face reached by each attachment, positions and fold onto a face already occupied and overlap it. Each of positions and folds onto an unoccupied face. Therefore of the nine positions work.
Thus, the correct answer is E.
Problem 13 in Other Years
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