Question

A \(100\text{ cm} \times 32\text{ cm}\) 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 \(100\text{ cm} \times 1\text{ cm}\).
The total number of creases visible when the sheet is unfolded is ............

• A. 32
• B. 5
• C. 31
• D. 63

Hint:

Repeated halving into \(2^n\) equal parts produces \(2^n-1\) crease lines when fully unfolded.

Answer 1

The Correct Option is C

Step 1: Each fold aligns the long edge with its opposite side; hence every fold halves the shorter side (32 cm). After 5 folds the shorter side becomes \(32/2^5=1\) cm, matching the final size \(100\times1\) cm.
Step 2: Unfolding reveals creases perpendicular to the long edge that partition the 32-cm side into \(2^5=32\) equal strips of 1 cm each.
The number of creases equals the number of partitions minus one: \(32-1=31\).
Therefore, the number of creases is \(\boxed{31}\).