Solution
Burning Ropes
Show the problem again
You have two ropes and a lighter. Each rope takes exactly 60 minutes to burn end to end, but burns non-uniformly (half the rope may take 5 minutes or 55). Using only these ropes, you can measure exactly 45 minutes. In the standard solution, what is the total number of rope ends you must light?
Worked solution
The answer is 4 rope ends. Light rope A at both ends and rope B at one end simultaneously (3 lightings). A rope lit at both ends burns in exactly half its time (the flames must meet after consuming everything, regardless of uniformity), so rope A finishes at 30 minutes. At that moment rope B has 30 minutes of burning left; lighting its second end (the 4th lighting) halves the remainder to 15. Total: 30 + 15 = 45 minutes. Three lightings can only mark 30 or 60 minutes, so 4 is minimal.
Source: Classic rope-burning timing puzzle in wide circulation; no traceable original source. Statement written for AxiomIQ.