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        riddles >> hard >> Alien Abduction
        
(Message started by: Enigami on Feb 14^th, 2010, 1:10pm)

Title: Alien Abduction
Post by Enigami on Feb 14^th, 2010, 1:10pm

20 people from around the earth are abducted by aliens and are locked in the mothership. They go through an experiment that tests their thinking capability . A random number ranging 1-20 is carved on each abductee's head (with repetitions allowed), and they are all put in a room which each one sees all the numbers excluding his own.The may not communicate in any way, nor physically see their number ( from a reflection for example). Then, each one is taken to a different room and asked about his number.If at least one answers correctly (the number on his head), the aliens acknowledge them as intelligent beings and are set free.
They are told about this experiment beforehand and can discuss a plan, and they happen to be mathematicians.
Find such a plan that always works.

short version:[hide]20 people are in a room and given random hats with numbers 1-20(with repetitions). each sees all the other hats but his own. They are all asked immediately, simultaneously and independently about the number on their hat. if at least one answers correctly, they win. They can discuss plan before hand. Find such a plan that always works [/hide]

Note: The only information each one can physically obtain is the other numbers.

Title: Re: Alien Abduction
Post by SMQ on Feb 14^th, 2010, 1:35pm

We've seen a similar problem (with 100 people) somewhere before--it's a neat mathematical trick: [hide]Beforehand each person picks uniquely one of the numbers from 0 to 19. After seeing all the other numbers, they each assume that the sum of all the numbers (mod 20) equals their chosen number, and guess the number on their head accordingly. One of them has to be correct.[/hide]

--SMQ

Title: Re: Alien Abduction
Post by Enigami on Feb 14^th, 2010, 2:01pm

I haven't seen it on the site or in the forum anywhere. But I have managed to solve it myself (the story is mine..). Broke a few brilliant minds to at work to desperation with this one.

Title: Re: Alien Abduction
Post by SMQ on Feb 15^th, 2010, 6:23am

No surprise you hadn't seen it: it's several years old and you would have to know what to search for. The original thread (with some interesting side discussion) is here (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1174688369).

--SMQ

Title: Re: Alien Abduction
Post by Enigami on Feb 15^th, 2010, 12:53pm

Thanks. I've actually been hanging around here for a while ( three years or so), and never took the minute to register (: