Galactic Riddles

Planet

A Sheet of Paper

An alien archivist from Staterion’s Office of Weights and Measures folds a very thin sheet of paper, with a stack of folds rising toward the starry sky, in front of Liz and M00N

Kinesys touches down, with surprising grace, on the roof of Staterion’s Central Office of Weights and Measures. Inside, among shelves of standards for every known unit, an archivist is carefully folding a very thin sheet of paper.

“Thickness: four thousandths of an inch,” he announces proudly. “I’m going to fold it 42 times.” Liz raises an eyebrow: “Why 42?”

M00N lights up all over: “Because it’s the Answer to the Ultimate Question of Life, the Universe, and Everything!” Dord snorts: quoting an Earth novel in a measurement office strikes him as a lack of rigor. Still, deep down, even he wants to know how tall the stack will be at the end.

The Riddle

Imagine you have a rectangular sheet of paper 0.004 inches thick and as large as you need. Fold it in half, so you get two half-sheets stacked on top of each other, and therefore double the thickness. Keep folding it in half, getting smaller and smaller sheets and thicker and thicker stacks. After 42 folds, imagine climbing onto the paper tower you’ve built. How high do you think you can go?

  1. You barely climb one stair step (about 8 inches)
  2. You reach the second floor of a house (about 10 feet)
  3. You conquer the summit of Everest (about 29,000 feet)
  4. You become the first paper folder on the Moon (about 239,000 miles)

P.S.: 42 isn’t a random number: it’s the Answer to the Ultimate Question of Life, the Universe, and Everything, from Douglas Adams’s novel The Hitchhiker’s Guide to the Galaxy.

Hint

Every fold doubles the thickness. For mental math: ten doublings multiply by about a thousand (210 = 1,024).

Solution

The answer is that you can go all the way to the Moon, and to tell the truth, a bit beyond.

Every fold doubles the thickness, so after 42 folds the total thickness is 242 times the original. Since 242 is about 4.4 trillion, the thickness becomes about 17.6 billion inches, or roughly 278,000 miles: more than the distance from Earth to the Moon, which is approximately 239,000 miles.

At this point you might wonder why anyone spends so much money on space missions, when you could just go to a stationery store, buy a sheet of paper, fold it 42 times, and climb on top. Liz, for the record, still prefers the teleporter, even though it always gets the destination wrong.