The prisoners have a chance to plot their strategy in advance, and they are going to need it, because unless every single prisoner finds his own name all will subsequently be executed.

Find a strategy for them which has probability of success exceeding 30%.

Comment: If each prisoner examines a random set of 50 boxes, their probability of survival
is an unenviable 1/2^{100} ∼ 0.0000000000000000000000000000008. They could do worse—if they all
look in the same 50 boxes, their chances drop to zero. 30% seems ridiculously out of reach—but
yes, you heard the problem correctly!