2005 PMWC Problems/Problem I10: Difference between revisions
Created page with "== 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 <math..." |
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If the string is not folded at all, exactly <math>1</math> cut will occur, splitting the string into <math>2</math> pieces. Thereafter, every time the string is folded in half doubles the number of cuts. So, if the string is folded in half <math>8</math> times, the single cut splits it in <math>2^8=256</math> places, resulting in <math>\boxed{257}</math> pieces. | If the string is not folded at all, exactly <math>1</math> cut will occur, splitting the string into <math>2</math> pieces. Thereafter, every time the string is folded in half doubles the number of cuts. So, if the string is folded in half <math>8</math> times, the single cut splits it in <math>2^8=256</math> places, resulting in <math>\boxed{257}</math> pieces. | ||
== See also == | ==See also== | ||
{{PMWC box|year=2005|num-b=I9|num-a=I11}} | {{PMWC box|year=2005|num-b=I9|num-a=I11}} | ||
Latest revision as of 20:56, 25 April 2014
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 
cut will occur, splitting the string into 
pieces. Thereafter, every time the string is folded in half doubles the number of cuts. So, if the string is folded in half 
times, the single cut splits it in 
places, resulting in 
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 | ||
