Measure Forty-Five Minutes with Two Unevenly Burning Ropes

Interview Prompt

You are given two ropes. Each one burns completely in exactly 60 minutes when lit from one end, but the burn rate is uneven and the two ropes may differ. Using only a lighter and no timepiece, outline a method that measures exactly 45 minutes.

Constraints & Assumptions

• Lighting one end of a rope does not mean half its length will burn in 30 minutes.
• At any observable event, you may light either end of either rope.
• The only timing signals are the moments when ropes finish burning.

Clarifying Questions to Ask

• Does each rope's total one-ended burn time stay exactly 60 minutes even though the burn is uneven?
• Can both ends of a rope be lit at the same time?
• Is the target interval measured from the first ignition?

What a Strong Answer Covers

• A series of lightings linked only to observable burn-completion events.
• Reasoning correctly about remaining burn time, not remaining rope length.
• A proof that uneven burn rates cannot alter the measured 45-minute interval.

Follow-up Questions

• What other exact durations can these same two ropes measure?
• Why is it invalid to mark the physical midpoint?
• Which assumption would break if lighting both ends changed the rope's chemistry?

Overview: Measure exactly 45 minutes with two ropes that each burn for 60 minutes but at unpredictable rates. The reasoning must depend only on lighting rope ends and observing completion events, never on assuming that half a rope corresponds to half the time.