The strings are not clocks: they burn capriciously, without respecting proportions or halves. And yet, with just a lighter and some ingenuity, they can measure time precisely.
The two ropes
Riddle statement
You have two ropes and a lighter. Each rope takes exactly one hour to burn completely, but it does not burn evenly: one half can take much longer than the other.
How can you measure exactly 45 minutes?
Show solution
Solution
Answer: Light one rope at both ends and the other at one end.
Call ropes A and B. At the same instant, light A at both ends and B at one end.
As A burns from both ends at the same time, it is consumed in 30 minutes, although its combustion is irregular.
When A goes out, B has been burning for 30 minutes. one extreme: it has exactly 30 minutes of combustion left. At that moment you light the other end of B.
By now burning on both sides, those remaining 30 minutes are consumed in 15 minutes.
In total you have measured: