If each prisoner randomly labels the boxes in their own (presumably independent) manner, then this strategy fails miserably. In fact, it's equivalent to each pr

If each prisoner randomly labels the boxes in their own (presumably independent) manner, then this strategy fails miserably. In fact, it's equivalent to each prisoner choosing 50 random (unique) boxes. The solution specifies that "the prisoners must first agree on a random labeling of the boxes by their own names." This is necessary.