Question

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?

$2$

$3$

$4$

$5$

$6$

Answer: E

Concepts:net (3D geometry)cube geometry

Difficulty rating: 1410

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.

2003 AMC 10A Problem 10

Answer: E

Difficulty rating: 1410

Solution:

Problem 10 in Other Years