Discussion
A 100 cm × 32 cm rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions 100 cm × 1 cm.
The total number of creases visible when the sheet is unfolded is _______.
Answer: C
The unfolded sheet shows 31 creases.
Each fold doubles the number of layers, and the 32 cm side is halved each time: 32, 16, 8, 4, 2, 1 cm after five folds, consistent with the final 100 cm × 1 cm strip. After 5 folds there are \(2^{5} = 32\) layers stacked across the original 32 cm width.
Unfolded, those 32 layers become 32 strips of 1 cm side by side, and 32 strips are separated by \(32 - 1 = 31\) creases.
32 counts the strips, not the lines between them; 5 counts only the folding operations, forgetting that later folds crease several layers at once; and 63 is \(2^{6} - 1\), the count for six folds.
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