Problem:
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?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If the polygon is folded before the fifth square is attached, then edges and must be joined, as must and . The fifth face of the cube can be attached at any of the remaining edges.\
The problems on this page are the property of the MAA's American Mathematics Competitions