You are in a gaggle of sixty prisoners, and the warden has a recreation to play with you.

In a room there are sixty packing containers. Each field can include both two apples, two oranges or one in all every, however you do not know which incorporates what number of. When the sport begins, every prisoner can go within the room and choose one fruit every from the entire packing containers (together with labelled ones). Then he’s allowed to place ‘2 Apples’, ‘2 Oranges’ or ‘Apple & Orange’ labels on as many packing containers as he needs. He is not allowed to alter the labels of labelled packing containers.

After that, they are going to be put in a soundproof room, with there is no such thing as a communication, one for each prisoner. When all of the packing containers are labeled, the prisoners are freed if they’re all positioned accurately, or exceuted in any other case.

You can merely examine each field, then label every one with the fruit you get, however you solely have a $(frac{2}{3})^{60} = 2.7197216 instances 10^{-11}$ likelihood of getting freed.

What is the optimum plan to maximise the possibilities of the prisoners being freed?