You are in a boat in the middle of a lake, with a steel anchor inside of the boat. You toss the anchor overboard, into the lake.

Did the water level of the lake rise, drop or stay the same?

You were enjoying a pleasant weekend on a luxury cruise liner when your ship was captured by pirates. These pirates don't like to take so many prisoners, so they decide to execute all... but one of you.

In a circle around a big pillar, the pirates have labeled 1000 positions, from 1 to 1000. Each captured passenger (including you!) is to choose one of the positions and stand under the respective number.

Once all passengers are in place, the pirates execute passenger #1. They then execute every OTHER person. So passenger #3 is next. They continue killing every other person, even continuing around the circle until finally 999 pasengers have been executed and only 1 is left, who is spared.

Assuming you actually want to be the one who lives, which numbered position will you choose?

You find yourself locked in a room which is filled with nothing but ropes of various length and composition. All of these ropes have inconsistent compositions and densities, even within themselves, but they all have one common property:

If you set a rope on fire from one end, it will take precisely one hour to burn to the other end.

It is important to note that because the ropes are warped, with inconsistent composition and density, they do not burn evenly. For example, if a rope has burned half its length, that does NOT necessarily mean that it has burned for half an hour.

There is an exit to the room, with a lever to operate the door. In order to open the door, you must first pull the lever and then the push it back into place precisely 45 minutes later.

With nothing but a lighter and knowledge of the hour burning ropes, how can you accurately time 45 minutes to open the door?