Measure Forty-Five Minutes with Two Unevenly Burning Ropes
Company: Meta
Role: Software Engineer
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
## Interview Prompt
You have two ropes. Each rope takes exactly 60 minutes to burn completely from
one end, but neither burns at a uniform rate and the ropes need not behave alike.
With only a lighter and no clock, describe a procedure that measures exactly 45
minutes.
### Constraints & Assumptions
- Lighting one end of a rope does not imply half its length burns in 30 minutes.
- You may light either end of either rope at any observable event.
- The only timing signals are ropes finishing their burns.
### Clarifying Questions to Ask
- Does each rope's total one-ended burn time remain exactly 60 minutes despite unevenness?
- Can both ends of a rope be lit simultaneously?
- Is the desired interval measured from the first ignition?
### What a Strong Answer Covers
- A sequence of ignitions tied only to observable burn-completion events.
- Correct reasoning about remaining burn time rather than remaining rope length.
- A proof that uneven burn rates cannot change the measured 45-minute interval.
### Follow-up Questions
- Which other durations can the same two ropes measure exactly?
- Why is marking the physical midpoint invalid?
- What assumption would fail if lighting both ends changed the rope's chemistry?
Overview: Measure exactly 45 minutes using two ropes that each burn for 60 minutes but at unpredictable rates. The reasoning must rely only on lighting rope ends and observing completion events, never on assuming that half a rope represents half the time.