Question

A 100 cm $\times$ 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 $\times$ 1 cm.

The total number of creases visible when the sheet is unfolded is ___________.
 

• A. 32
• B. 5
• C. 31
• D. 63

Hint:

Folding the same dimension $n$ times creates $2^n$ equal segments and therefore $2^n-1$ crease lines upon unfolding. If dimensions confirm ($\text{original}/2^n$), you’re on the right track.

Answer 1

The Correct Option is C

Step 1: Understand the fold direction. Each fold aligns the two long (100 cm) edges, so the fold axis is parallel to the long edge and halves the 32 cm side every time.
Step 2: Compute final thickness along the folded dimension. After $5$ folds: $32 \div 2^5 = 32 \div 32 = 1$ cm, matching the statement.
Step 3: Count creases after unfolding. Repeated halving along the same direction divides the sheet into $2^n$ equal strips along that direction, separated by straight crease lines.
Hence, with $n=5$ folds, the number of crease lines $= 2^5 - 1 = 31$.
\[ \boxed{31} \]