Puzzle

Let’s look at the pattern we get by folding. After the first fold, the result is 2 sheets thick. After the second fold, it is 4 sheets thick, then 8, then 16 and so on:

2, 4, 8, 16 . . .

This sequence may be written as powers of 2:

2¹, 2², 2³, 2⁴. . .

If we fold 50 times, the thickness of the final result is 2⁵⁰ sheets. How thick is this?

We measured the thickness of a one ream package of paper we had here in the office. It was 5 cm (2 in) thick. Since there are 500 sheets in a ream, each sheet is 0.01 cm (.004 in) thick.

Now 2⁵⁰ is a very large number. It equals 1.1259 x 10¹⁵. This may also be written as

1,125,900,000,000,000

That’s a very thick pile of paper! Since each sheet is 0.01 cm thick, we can divide our result by 100 to find out how high it is in cm:

11,259,000,000,000 cm (4,432,677,165,400 in)

It’s still hard to imagine how big this is, so let’s divide by 100 again to convert to m:

112,590,000,000 m (369,389,763,780 ft)

Maybe we should try km. There are 1,000 m in a km, so dividing by 1,000 we have:

112,590,000 km (69,960,183 mi)

The distance from the Earth to the Sun is about 150,000,000 km (93,205,679 mi)

Does this result surprise you?