How many paper folds to reach the Sun?

Question

A sheet of paper is 0.1 mm thick, and each fold doubles the thickness. Solve in your head. How many folds until the stack reaches the Sun (\approx 1.5 	imes 10^{8} km)? Aim: under 30 seconds.

Accepted Answer

Target in sheet-thicknesses: \frac{1.5 	imes 10^{8} 	ext{ km}}{0.1 	ext{ mm}} = \frac{1.5 	imes 10^{11} 	ext{ m}}{10^{-4} 	ext{ m}} = 1.5 	imes 10^{15}. Count doublings with 2^{10} \approx 10^{3}: - 2^{50} = (2^{10})^{5} \approx 10^{15} 	imes 1.13 \approx 1.13 	imes 10^{15}, just short. - 2^{51} \approx 2.3 	imes 10^{15}, past the Sun. About 51 folds. Here is the striking part: the Moon took about 42 folds, and the Sun is roughly 400 times farther, yet it costs only about 9 more folds. Multiplying the distance by 400 (about 2.6 orders of magnitude) adds only \log2(400) \approx 8.6 d…

How many paper folds to reach the Sun?

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