MathDB

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? [asy]unitsize(10mm); defaultpen(fontsize(10pt)); pen finedashed=linetype("4 4");
filldraw((1,1)--(2,1)--(2,2)--(4,2)--(4,3)--(1,3)--cycle,grey,black+linewidth(.8pt)); draw((0,1)--(0,3)--(1,3)--(1,4)--(4,4)--(4,3)-- (5,3)--(5,2)--(4,2)--(4,1)--(2,1)--(2,0)--(1,0)--(1,1)--cycle,finedashed); draw((0,2)--(2,2)--(2,4),finedashed); draw((3,1)--(3,4),finedashed); label("

1

",(1.5,0.5)); draw(circle((1.5,0.5),.17)); label("

2

",(2.5,1.5)); draw(circle((2.5,1.5),.17)); label("

3

",(3.5,1.5)); draw(circle((3.5,1.5),.17)); label("

4

",(4.5,2.5)); draw(circle((4.5,2.5),.17)); label("

5

",(3.5,3.5)); draw(circle((3.5,3.5),.17)); label("

6

",(2.5,3.5)); draw(circle((2.5,3.5),.17)); label("

7

",(1.5,3.5)); draw(circle((1.5,3.5),.17)); label("

8

",(0.5,2.5)); draw(circle((0.5,2.5),.17)); label("

9

",(0.5,1.5)); draw(circle((0.5,1.5),.17));[/asy]

<span class='latex-bold'>(A)</span>\ 2 \qquad <span class='latex-bold'>(B)</span>\ 3 \qquad <span class='latex-bold'>(C)</span>\ 4 \qquad <span class='latex-bold'>(D)</span>\ 5 \qquad <span class='latex-bold'>(E)</span>\ 6

10

Problems(2)