Zero Knowledge in the Cave

[Eric Cordian]

Nomen postulates:

> Following his instructions, you leave the entry room for a few minutes,
> while the explorer enters one of the passageways.  You then re-enter the
> room, and loudly call out one of the passageway numbers, either 1 or 2.
> In a few minutes, the explorer comes out of the requested passageway.
> You then leave the cave and repeat the process many times.  Each time, the
> reporter enters one of the passageways unknown to you; when you return and
> name one of them, he is able without fail to exit from the named passage.

> You reason that if there were no connection between the passageways,
> the only way the explorer could come out the passage that you named
> would be if he had gone in that same one.  He would have to guess
> which one you were going to choose, and if he were right, he could
> come out that one.  But you have repeated the test dozens of times.
> The chances that someone could guess right so often is infinitisimal.
> The only logical explanation is that the passageway does exist.

A more interesting question would be:  If there is no connection between
the passageways, and if the explorer manages to pick the passage you are
going yell out correctly a large number of times, would you be better off
betting or not betting $1 against him being able to do it again at 1000:1
odds.

-- 
Eric Michael Cordian 0+
O:.T:.O:. Mathematical Munitions Division
"Do What Thou Wilt Shall Be The Whole Of The Law"