You are in a group of sixty prisoners, and the warden has a game to play with you.
In a room there are sixty boxes. Each box can contain either two apples, two oranges or one of each, but you don't know which contains how many. When the game starts, each prisoner can go in the room and pick one fruit each from two of the boxes (including labelled ones). Then he is allowed to put '2 Apples', '2 Oranges' or 'Apple & Orange' labels on one or two of them (if they are unlabeled). EDITED: He is also allowed to change the labels of up to two boxes he didn’t look in. When all 60 prisoners have visited the room and there is at least one unlabeled box, the process starts again from the first prisoner.
After that, they will be put in a soundproof room, with there is no communication, one for every prisoner. When all the boxes are labeled, the prisoners are freed if they are all placed correctly, or exceuted otherwise.
You can simply have every box checked, then label each one with the fruit you get, but you only have a $(\frac{2}{3})^{60} = 2.7197216 \times 10^{-11}$ chance of getting freed.
What is the optimal plan to maximise the chances of the prisoners being freed?