Let us assume that you are an Atlas. We won't ask you to support 
the world.  Uncle Sam already does that.  All we ask you to do is 
to take a gigantic piece of cigarette paper and tear it in half. 
Next, put the two pieces on top of each other and tear them in two. 
Then put the ensuing four pieces on top of each other and tear them 
in two.  Follow this procedure 32 times until you have a large stack 
of cigarette paper.  This will have required a considerable use of 
your muscles.  Now flex your mental muscles and make an approximate 
guess as to how high the pile would be.  Would it be a foot, a yard, 
a mile or what? 
 
 

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                  THE SOLUTION
 

APuzzlezone.com's answer is that it would reach beyond the moon.

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My answer is that the paper pile would be almost 67 miles high.
Below are my sources and calculation.

From: http://www.bbc.co.uk/dna/h2g2/A1093420
   I learned that cigarette papers come in a variety of thicknesses
   - from the ultra thin such as Rizla Blue and Club, through to the
   heavyweights like Zig Zag and Rizla White.

From: http://www.patentstorm.us/patents/6817365/description.html
   I learned that typically, the cigarette paper is around 0.05 mm
   to about 0.5 mm in thickness.

Using the thinnest cigarette paper like Rizla Blue, the thickness
would by 0.05 mm.

One layer would be 0.05 mm

Two layers would be 0.10 mm or 0.05 mm x 2

Three layers would be 0.20 mm or 0.05 mm x 4 or 0.05 mm x 2²

Four layers would by 0.40 mm or 0.50 mm x 8 or 0.05 mm x 2³

Five layers would by 0.80 mm or 0.05 mm x 16 
   or 0.05 mm x 2 to the power of 4

thus

Thirty-two layers would by 0.05 mm x 2 to the power of 31
   which = 1.07374 x 10^8 mm

but
   1 mm = 0.0032808399 feet
   and
   1 mile = 5280 feet
so

Thirty-two layers = 1.07371 x 10^8 x 0.0032808399 ft/1 mm x 1 ft/5280 mi
                  = 66.7192 miles or about 67 miles