South African Mathematics Olympiad

Question

It is said that you can only fold a piece of paper in half 7 times. Harold folds a sheet of paper in half 5 times and then makes a hole in the folded paper. How many holes does the sheet of paper have after it is unfolded again? (A) 32 (B) 36 (C) 81 (D) 50 (E) 64

Accepted Answer

Each fold doubles the number of layers that will be pierced. There will be 2^5 layers and therefore 2^5 = 32 holes.