VLSI DV Interview Puzzles · All levels

Burning Ropes to Measure 45 Minutes

You have two ropes. Each rope takes exactly 60 minutes to burn, but burns non-uniformly. Measure exactly 45 minutes.

Puzzle

Difficulty: Medium · Puzzle 3 of 6 · Topic: Classic Brain Teasers

You have two ropes. Each rope takes exactly 60 minutes to burn, but burns non-uniformly. Measure exactly 45 minutes.

Hint

Lighting both ends changes remaining burn time predictably.

Step-by-step solution

diagram

1) Light rope A at both ends and rope B at one end at time t=0.
2) Rope A finishes in exactly 30 minutes (both ends lit).
3) At t=30, rope B has some length left, but that remainder would take exactly 30 more minutes from one end.
4) Light the other end of rope B at t=30; now remaining part burns in 15 minutes.
5) Total elapsed time is 30 + 15 = 45 minutes.

Answer

Answer: Light A from both ends and B from one end; when A finishes, light B's other end and wait until B finishes: 45 minutes total.

Why candidates get it wrong

Assuming non-uniform burn makes all timing impossible; total burn-time invariants still hold.

Interviewer follow-up

How would you measure exactly 15 minutes with the same two ropes?

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