Yes - the answer is much smaller than you'd expect.
This is because the doubling number sequence gets very large very quickly.
No-one would expect you to do this one in your head so, make a guess and then grab a calculator or a spreadsheet.
Start with 0.1mm - the average thickness for a piece of copy paper.
The answer is 27 times. After this many folds, the wad would be 13.4km thick. Everest is just under 8.9km tall.
Incredibly, folding it 42 times would make the wad as thick as the distance from Earth to the Moon.
Is this right? How many times can you fold a real piece of paper? Is the moon always the same distance from the Earth? For more on this conundrum, look here.
We'd love to hear your comments and suggestions on this or other brainteasers.