The challenge
You have two ropes. Each takes exactly 60 minutes to burn, but neither burns at a uniform rate. With a lighter and no clock, how can you measure exactly 45 minutes?
Two Ropes and 45 Minutes Puzzle
Solve this medium lateral challenge, then compare your reasoning with the hint, checked answer, verification, and variation.
Hint
Burning a rope from both ends changes its total burn time even when its rate is uneven.
Use completion events as the clock
The 45-minute event sequence
- Light both ends of the first rope and one end of the second at the same moment.
- When the first rope finishes, exactly 30 minutes have passed.
- Light the second end of the remaining rope; it finishes 15 minutes later.
Light both ends of the first rope and one end of the second. The first rope finishes after 30 minutes. At that moment, light the other end of the second rope. Its remaining portion now burns from both ends and finishes 15 minutes later. Total: 45 minutes.
Why equal lengths do not mean equal times
Cutting a rope in half does not create two 30-minute pieces because the rope does not burn at a uniform rate.
Timing invariant
Burning from both ends guarantees a rope finishes in half its one-ended burn time, regardless of how the burn speed varies along its length.
Measure events when rates are unreliable
Transform an unreliable rate into a reliable completion event.
How confident were you?
Replace length with known completion times
Do not try to measure rope length. An uneven rope gives no reliable length-to-time conversion. Instead, create known completion times by choosing how many ends are burning.
Measure a shorter interval
With the same two ropes, can you mark a 30-minute interval? Identify which lighting step is no longer needed.
Study lateral thinking techniques for the reusable method behind this challenge. Then explore the lateral thinking challenges learning path for connected examples and practice.