Interactive logic puzzle

Rope-Burning Puzzle

You have two ropes. Each takes exactly 60 minutes to burn from one end, but neither burns uniformly along its length. Use them to measure exactly 45 minutes.

Rope A

light both ends

Burning ×2

60 burn-min left

Rope B

one end first

Burning ×1

60 burn-min left

0 minTimeline45 min

30:00

45:00

Time

What to do

Light both ends of Rope A and one end of Rope B.

Rope A is being consumed at twice the total burn rate, so it finishes after 30 minutes.

Key insight

0 → 30: Rope A burns from both ends. Rope B burns from one.

At 30: Rope A is gone. This is a reliable 30-minute signal.

30 → 45: Light Rope B’s second end. Its remaining 30 burn-minutes are consumed in 15 minutes.

Measured time

30 + 15 = 45

The ropes need not burn uniformly along their physical length. The only assumption is that each rope takes exactly 60 minutes to burn completely from one end.

The moving burn fronts are illustrative; their spatial speed is not meant to imply uniform burning.

Based on the classic rope-burning puzzle described on Wikipedia.