2003 AMC 12A Problem 13
Below is the professionally curated solution for Problem 13 of the 2003 AMC 12A, 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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Difficulty rating: 1530
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?
Solution:
A cube missing one face has faces, so the fifth square must complete a foldable arrangement.
Folding the four-square piece wraps it around four faces of a cube, identifying two of its edges. The fifth square then folds up onto a face exactly when it is attached along one of the free edges.
Of the nine indicated positions, of them work.
Thus, the correct answer is E.
Problem 13 in Other Years
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