You find yourself trapped in a room with a time bomb set to go off in exactly 45 minutes. The bomb is located in a safe, but you don’t know the combination. You notice two ropes hanging from the ceiling, and a note nearby that reads:
“These are the only two ropes in the room. Each rope burns from one end to the other in exactly 60 minutes, but the rate of burning is not uniform. One half of the rope may burn in only 10 minutes, while the other half takes 50 minutes to burn. You must use these ropes and a lighter to measure exactly 45 minutes. Good luck!”
With the clock ticking, you frantically try to figure out how to use the ropes to measure exactly 45 minutes and disarm the bomb before it’s too late.
Here’s one solution that can be used to measure exactly 45 minutes using the two ropes:
1. Light both ends of the first rope and one end of the second rope at the same time.
2. The first rope will burn completely in 30 minutes, and the second rope will have burned halfway in the same amount of time (i.e., 30 minutes).
3. At this point, light the second end of the second rope. It will take an additional 15 minutes for the second rope to burn completely (since the first half took 30 minutes to burn and the second half will take another 30 minutes to burn, but it’s already been burning for 30 minutes, so only 15 minutes remain).
4. Once the second rope has burned completely, exactly 45 minutes will have passed. Use this time to open the safe, disarm the bomb, and get out of the room!
This solution works because the first rope burns completely in 30 minutes, which is halfway between 10 and 50 minutes. By lighting the second rope at the same time, it ensures that we can measure up to 60 minutes. By then lighting the second end of the second rope after 30 minutes, we ensure that only 15 minutes remain for it to burn completely, giving us a total of 45 minutes.