Question

Suppose one of the eight lettered identical squares is included with the four shaded squares in the T-shaped figure shown. How many of the resulting figures can be folded into a topless cubical box?

$2$

$3$

$4$

$5$

$6$

Solution:

The four shaded squares fold into four faces of an open box, and the added square supplies the fifth face. Picturing the folds, the squares $A,$ $E,$ $H,$ $B,$ $D,$ and $F$ each complete a valid topless box.

The squares $C$ and $G$ do not work, because folding would force four faces to meet at a single corner. That leaves $6$ valid figures.

Thus, the correct answer is E .

1986 AMC 8 Problem 21

Solution:

Problem 21 in Other Years