A 100 cm x 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 x 1 cm. The total number of creases visible when the sheet is unfolded is ___________.
A. 32
B. 5
C. 31
D. 63
GATE 2023 · General Aptitude · Paper Folding · medium
Answer: The total number of creases visible when the sheet is unfolded is 31.
Verify the number of folds from the dimensions: We need 32 / 2^n = 1, so 2^n = 32, giving n = 5. This confirms 5 folds along the 32 cm direction.
Count creases added at each fold: Fold 1: 1 new crease (divides sheet into 2 sections). Fold 2: 2 new creases. Fold 3: 4 new creases. Fold 4: 8 new creases. Fold 5: 16 new creases. Total = 1 + 2 + 4 + 8 + 16 = 31.
Apply the closed-form formula: For n = 5: total creases = 2^5 - 1 = 32 - 1 = 31.