# How to Measure 45 minutes using two identical ropes ? || Popular Interview Puzzle

Puzzle Details

How do we measure forty-five minutes using two identical ropes, each of which takes an hour to burn? We have matchsticks with us. The ropes burn non-uniformly. So, for example, the two halves of the rope might burn in 10 minutes and 50 minutes respectively

Solution:

The ropes are non-uniform, which means that if we cut a rope in two halves, then both halves may not take 30 minutes each to burn (But on a whole the rope will take 60 minutes to burn).

The above approach is not going to help. To calculate 30 minutes, you only need 1 rope to burn the rope from both ends, it will take the rope 30 minutes to burn completely. To calculate 45 minutes, you need 2 ropes, Let's call the ropes A & B. Follow the below process:

Burn Rope-A from both ends and Rope-B from one end. Rope-A will completely burn in 30 minutes (because it is put on fire from both ends). When Rope-A is burnt completely, Rope-B would have burnt for 30 minutes (It does not mean that Rope-B is half burnt), At this point lit the other end of Rope-B as well, it will take another 15 minutes for Rope-B to burn completely.

In Short, Light up three of the four ends of the two Ropes. Once one Rope is completely burnt, light up the fourth end. At 45 minutes, both Ropes are burnt completely.

watch the below video for more detailed observations.