Hello. I am a machine, robot. My Master is doing an experiment with me. They ask me to choose between two doors A and B. Death awaits me behind one of the doors. And I do not want to choose that one. The difficult part is that the master made a clone of me previously and did this experiment with my clone. Now Master put Death behind the door my clone have had chosen. So if my clone chose the door A, then Death is behind the door A. I cannot use any environment information to make my decision, only my internal reasoning – that is part of the experiment.
Had the clone not been told that he also had a clone, he would have chosen the door A; then I have to choose B. But if the clone had been told that he had been cloned as well and the clone of the clone did not known about being cloned, then my clone’s selection must be B and my selection have to be A. This means that my selection must depend on the depth of knowing which of the clone’s clone did not know about being cloned - whether it is odd or even.
The real problem is that my clone got exactly the same information as myself. Whatever I choose, that must be the same as the selection of my clone. So the Death will be behind the door I will choose. Whatever door I choose! I cannot deceive myself and choose the other, because any my reasoning had already been simulated.