Problem 302

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Problem 302: (2003 AMC 10a, 10; 12a 13)

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?

$\mathrm{(A) \ } 2\qquad$ $ \mathrm{(B) \ } 3\qquad$ $ \mathrm{(C) \ } 4\qquad$ $ \mathrm{(D) \ } 5\qquad$ $ \mathrm{(E) \ } 6$

Solution

Exercise 302: Solution

Four congruent squares form the gray T-shaped figure shown. A fifth congruent square is attached at one of the eight labeled positions. How many of the resulting shapes cannot be folded to form a cube with one face missing?

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