Discussion
A planar rectangular paper has two V-shaped pieces attached as shown below.
This piece of paper is folded to make the following closed three-dimensional object.
The number of folds required to form the above object is
Answer: A
The number of folds required is 9.
The two V-shaped pieces become the front and back faces of the solid, and the long strip wraps round the edge of the V to form its sides. The V outline has 8 edges: the outer slant, flat bottom and outer slant on the outside, the two flat arm ends, and the inner slant, inner bottom and inner slant of the notch. So the strip must provide 8 side faces.
Turning 8 side faces into a closed band takes a fold between each neighbouring pair: 7 folds along the strip. Each V-piece must then be folded over onto the band, which adds 2 more:
\[ 7 + 2 = 9 \]
7 counts only the folds along the strip, 8 adds just one of the V-pieces, and 11 counts more side faces than the V outline has.
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