Jon Pretty

There are 100 prisoners, numbered 1-100. The prisoners' numbers are written onto 100 cards, put randomly into 100 envelopes numbered 1-100. They can't communicate, but are invited, one by one, to open 50 envelopes. If any prisoner fails to find his number, they all get killed.

At best, there's a 50% chance any one prisoner can find his number. It would seem like there's a probability of (½)¹⁰⁰ or 0.00000000000000000000000000008% that every prisoner could find his own number, if each were to check 50 envelopes at random.

So, if it were 2 prisoners opening 1 envelope I would tell them to start with envelope with the same number as their position in line

That (or the isomorphic strategy) would be the perfect strategy for two prisoners, and they would have a 50% chance of survival.

What about four prisoners opening two envelopes?