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Escape from prison

Escape from prison

Two friends are convicted of a crime they did not commit in the safest prison in the world located on top of a large mountain. They are forced to work from sun to sun by a miserable piece of bread and a glass of water a day under the supervision of the evil prison director.

One day they receive a mysterious message from a prisoner who managed to escape long ago. The message read as follows: A horse rests behind the prison walls that will follow the path that leads to my house and is exactly fifteen minutes away from the prison. Be precise with the travel time since otherwise you will not be able to locate my den. In my house you will receive shelter and food.

Our friends want to take advantage of the relief of the guard to escape from the prison by filing the bars of the window of the cell that overlooks the back of the prison where the horse is located and that is poorly guarded. The problem is that they do not have a clock or any gadget that allows them to calculate the exact time (15 minutes to get to the house) and can not risk being wrong because the area is inhabited by the prison director's minions .

Javier and Carlos are smokers and have two wicks of poor quality and a lighter each. They know that each wick takes exactly one hour to burn completely and that it does it irregularly, that is, once it is lit it can burn half a wick in 10 minutes and the other half in 50 minutes, for example.

How will our friends calculate exactly the time (15 minutes) exactly with the wicks they have in order to carry out their escape successfully?

Solution

Since the wicks burn irregularly we cannot cut them proportionally to the time we need to calculate. We know that if we light one of the wicks at one end it takes exactly one hour to burn completely so that if we light the wick on both sides the time it will take to burn completely will be half, that is, half an hour.

Simultaneously, the first wick is lit on both sides and the second by one end. When the first wick (which has been lit at both ends) is completely consumed, the second wick goes out. In this way, we have a piece of wick that takes exactly half an hour to burn, so if they light it on both sides at the time of starting the trip they will be able to calculate the exact fifteen minutes they need to make the escape a success.