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So here is the deal:

There is a team of 16 people. There are 16 rooms and there is another room with a box with gold in it. The team knows that the box is closed at the beginning. After that each team member is locked in a room and they do not have any contact with each other. Randomly one player is picked, he can go to the room with the box in it and he can decide if he wants to open it, close it or leave it so that it was when he entered the room. After that this player have to go back his room and a next player is picked randomly. The procedure repeats itself until somebody claims that now all of the team member were at least once in the room with the box in it. If it is true they win the gold form the box, if not they don't. Which strategy should the team apply to win?

Can anybody give me an idea how should I start to think? Is it possible to solve it as a model of a Turing-machine?

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    Can the same player be called twice? Or is it only once – 2017-02-06
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    @GautamShenoy: the problem would be rather easy if nobody could be called more than once :-) – 2017-02-06
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    I think there is no connection to turing machines. The central role in this puzzle is that each round the player is picked randomly. – 2017-02-06
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    @GautamShenoy they can be called more than once. – 2017-02-06
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    @GautamShenoy : If nobody can be called twice, then it would be impossible for anybody to recognize that he is the last one to be picked. – 2017-02-06
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    @TonyK is right, the 100 prisoners is the quite the same – 2017-02-06
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    @Thorsten: You missed the point: if nobody can be called twice, then the whole thing will be over after exactly 16 rounds. – 2017-02-06

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