About two years ago, Veritasium posted The Riddle That Seems Impossible Even If You Know The Answer on Youtube. Today i was rewatching that video, because after seeing it initially i had some doubts, and it was a bit of an itch i finally decided to scratch.

The basic riddle goes something like this (watch the video for a much more coherent explanation AND the solution):

  1. You have 100 prisoners, each with a number.
  2. There is a room with 100 (numbered) boxes, and every prisoner number is in one random box.
  3. Prisoners enter the room one by one
  4. Each prisoner can open 50 boxes and search for their prisoner number.
  5. Each prisoner has to leave the room exactly as he found it.
  6. If ALL prisoners find their own number, everyone goes free.
  7. If even a single prisoner fails to finds his number, everyone stays in jail.
  8. Prisoners can decide on a tactic BEFORE the event, but can't communicate in any way DURIN the event.

If prisoners just do random sampling, their chances are 0.5**100 = 0.0000000000000000000000000000008.

Is there a better tactic? (Rest of the post in spoiler tags if you want to have a go on the problem yourself).

<Reveal this spoiler or all in this thread>

Frankly, even having programmed a full simulation of the solution myself, it still absolutely boggles my mind that this actually works at all. Maths is weird.

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In reply to Proving Veritasiums riddle using Perl by cavac

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