mathschallenge.net

Problem

A piece of string measures 2/3 m. Without the use of any other measuring tools, how would you use the string to measure 1/2 m?

Solution

Begin by folding the string in half along its length; this will be 1/3 m.
Fold the 1/3 m length in half, giving 1/6 m.
Finally fold the 1/6 m length back along the length of the string.
The remaining length will be 2/3 1/6 = 1/2 m.

What if you wanted to measure 1/4 m using the same piece of string?
What about 1/5 m?