A3 How many times must we fold a sheet of paper so that the stack has 512 sheets?
(A) five times
(B) seven times
(C) nine times
(D) ten times
(E) none of the above
A3. Thinking: If we fold a sheet once, we get 2 sheets, with two folds we get $4=2^{2}$ sheets, with three $8=2^{3}$ sheets, with $n$ folds $2^{n}$ sheets. The paper must have 512 sheets after $n$ folds, so $2^{n}=512$. We write this with powers of the same base $2^{n}=2^{9} . n=9$ The sheet must be folded nine times.