2003 AMC 10A Problem 10

Problem 10 of 25EasierGeometry

The polygon enclosed by the solid lines in the figure consists of

4

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?

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Solution

Fold the four shaded squares first. They occupy four distinct faces of the cube, leaving two faces open. Checking the numbered attachments, positions

1,

2,

and

3

fold the new square onto a face already occupied by one of the shaded squares. Positions

4,

5,

6,

7,

8,

and

9

fold it onto one of the two open faces. Therefore exactly

6

of the

9

polygons work. Thus, the correct answer is E.

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