100 Prisoners Escape Puzzle

Recently, I wrote about a classic prisoner escape puzzle which, at first glance, appeared impossible. There’s another classic, impossible sounding, prisoner escape puzzle called the 100 prisoner problem. It was first written about by Danish computer scientist Peter Bro Miltersen. In this puzzle there are 100 prisoners, each given a distinct number 1-100. The jailer has decided to give all the prisoners a chance to escape. He prepares a challenge, and if every single one of the prisoners passes, they are all free to go. If even one of them fails, they all die.
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