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        riddles >> medium >> Five red discs
        
(Message started by: pcbouhid on Nov 26^th, 2005, 6:10am)

Title: Five red discs
Post by pcbouhid on Nov 26^th, 2005, 6:10am

Paul shows nine colored discs (five red, two blue and two green) to five logicians.

After blindfolding them, Paul picks up the five red discs, sticks one on the forehead of each logician, and hides the other discs elsewhere. After removing the blindfolds, everyone sees the discs (all red) on the others' foreheads but not the one on his own.

After a few minutes of thinking, all the logicians (that we assume for the purpose of this problem, reasons at the same speed) correctly states the color of theirs own discs, at the same time. How does they work it out?

Title: Re: Five red discs
Post by rmsgrey on Nov 26^th, 2005, 6:48am

I'm not convinced that this is solvable without some form of synchronization - if the logicians don't each know the speeds at which the others reason, then they have trouble judging how long it requires for each iteration. After four iterations, the knock-on effect of the uncertainties is almost certainly too high.

Even if the logicians all know how fast they each reason, there's still a leap to the general case to take into account - once you've worked out what would happen with exactly three red discs out there, you should know what would happen with 100 logicians and any number of red discs up to 100 (given there are exactly 99 non-reds in the original pool) - assuming you can get around the synchronization problem.

Of course, if you have any form of synchronization, then all 5 would speak at once.

Title: Re: Five red discs
Post by pcbouhid on Nov 26^th, 2005, 8:15am

Ok, I´ll rephrase the text with an assumption whose purpose is only for this problem (there´s no way to measure this).

Title: Re: Five red discs
Post by Icarus on Nov 26^th, 2005, 11:17am

A better choice would be to have Paul ask "does anyone know their color?" repeatedly, until suddenly all five answer "yes".

I also thought about suggesting not telling that all got red discs in the puzzle, since this can be deduced from their simultaneous answer. But then I realized that including this information actually makes the puzzle more tricky, since to solve it, you must consider [hide]situations you already know to be false[/hide] - something most people don't do.

Title: Re: Five red discs
Post by rmsgrey on Nov 27^th, 2005, 8:31am

Of course, if you recognise the problem, it becomes trivial (just ask the brown-eyed monks!)

Title: Re: Five red discs
Post by Icarus on Nov 27^th, 2005, 10:28am

Well, I was going to ask the red-eyed monks. I even stopped by the monastery to say that I had a question for them, which I would ask when I had more time. But when I stopped in again several days later, I couldn't find any red-eyed monks, and the browned-eyed monks were all too busy digging graves in the graveyard to help me. Besides which, from the looks they were giving me, you'd think I'd killed someone!