2005 PMWC Problems/Problem I10

Problem

A long string is folded in half eight times, then cut in the middle. How many pieces are obtained?

Solution

If the string is not folded at all, exactly $1$ cut will occur, splitting the string into $2$ pieces. Thereafter, every time the string is folded in half doubles the number of cuts. So, if the string is folded in half $8$ times, the single cut splits it in $2^8=256$ places, resulting in $\boxed{257}$ pieces.

See also

2005 PMWC (Problems)
Preceded by
Problem I9
Followed by
Problem I11
I: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T: 1 2 3 4 5 6 7 8 9 10
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