Fold paper 42 times to reach the Moon: solved step by step

Problem. A sheet of paper is 0.1 mm thick and every fold exactly doubles the thickness, so after n folds it is 0.1 mm × 2^n. How thick is the stack after 42 folds, and is that more than the 384,400 km to the Moon?

Step by step

1. Each fold doubles the stack, so after n folds the thickness is 0.1 mm × 2^n.

2. After 7 folds: 2^7 = 128, so the thickness is 0.1 mm × 128 = 12.8 mm, about the width of a finger.

3. After 23 folds: 2^23 = 8,388,608, so the thickness is 0.1 mm × 8,388,608 ≈ 839 m, taller than the CN Tower (553 m).

4. After 27 folds: 2^27 = 134,217,728, so the thickness is about 13,421,773 mm ≈ 13.4 km, higher than a plane cruises (about 11 km).

5. After 42 folds: 2^42 = 4,398,046,511,104, so the thickness is 0.1 mm × 4,398,046,511,104 ≈ 439,804,651,110 mm.

6. Convert to kilometres by dividing by 1,000,000 (1 km = 1,000,000 mm): 439,804,651,110 mm ÷ 1,000,000 ≈ 439,805 km.

7. Compare with the Moon: 439,805 km − 384,400 km ≈ 55,405 km, so the stack passes the Moon's distance with room to spare.

Answer: After 42 folds the stack is 0.1 mm × 2^42 ≈ 439,805 km thick, farther than the Moon (384,400 km).

This is an idealized calculation: real paper cannot be folded 42 times, because the stack gets too thick and too short to fold and each fold loses length, so the result shows the power of doubling, not a physical experiment.