This classic logic puzzle challenges you to measure exactly 45 minutes using just:

  • 2 ropes, each taking exactly 1 hour to burn end-to-end,
  • A lighter, and
  • The knowledge that the ropes burn non-linearly (i.e., not at a consistent rate).

Constraints

  • You cannot fold or cut the ropes.
  • You cannot assume uniform burning.
  • But you can light either or both ends of either rope at any time.

The Strategy

Here’s the clever trick: leverage the doubling of burn rate when lighting both ends.

Step-by-Step Solution

  1. Light Rope A at both ends and Rope B at one end simultaneously.

    • Rope A will burn twice as fast and take exactly 30 minutes to be consumed.

  2. As soon as Rope A finishes burning (after 30 minutes), immediately light the other end of Rope B.

    • At this point, Rope B has burned for 30 minutes from one end, so half remains—but again, due to irregular burn rate, we don’t know where the flame is.
    • Lighting the other end now causes it to burn from both ends, which doubles the burn rate of the remaining segment.

  3. The remaining rope will now take 15 minutes to finish burning.

    • 30 minutes + 15 minutes = 45 minutes in total.

Why It Works

Even though the burn rate is inconsistent, lighting both ends guarantees a known time: the rope burns completely in half the original time regardless of rate variability. That’s the core trick.

Final Answer

Light Rope A at both ends and Rope B at one end. When Rope A finishes (30 min), light the other end of Rope B. When Rope B finishes, 45 minutes have passed.

Reference