# Fun Brainteaser

Diffy
Hey all,

I came across this fun little brainteaser, I hope you all enjoy!

You are given two pieces of rope, and a book of matches. The two pieces of rope are in no way alike, they are different lengths and widths. All you know about the two pieces of rope is that if you were to light one on fire it would take an hour to burn from end to end. The rate at which the ropes burn are different, and the rates are not constant. That is to say, for example, it could take 5 minutes to burn half way, and then another 55 minutes to burn the other half. Furthermore the two ropes do not burn at the same rate.

The challenge then is to say when exactly 45 minutes have elapsed, using only the two ropes, and your matches.

Let me know if any part of this needs clarification.

Enjoy!

LukeD
Hmm...

No calculations here, so this might be wrong, but I'm going to write what I think is a valid solution (solution should be hidden, highlight to read).

Designate one rope to be rope 1 and the other to be rope 2. Simultaneously light both ends of rope 1 and one end of rope 2. As soon as rope 1 finishes burning, light the other end of rope 2. When rope 2 has finished burning, exactly 45 minutes have passed.

Rope 1 finishes burning at half an hour. At this point, rope 2 will be half burned (time wise - not necessarily length wise), so it would take another 30 minutes for it to finish burning if we did not burn the other end. Lighting the other end causes it to burn twice as fast, so it burns in 15 more minutes.

NZer
Yep that's pretty much what I thought as well, so it has a pretty good chance of being right :D

Diffy
Yes that is the correct solution!

armis
That's a nice one. I remember we got exactly the same one at school during a math class