bonanova Posted March 30, 2008 Report Share Posted March 30, 2008 A wizard selects three excellent logicians and places hats on their heads. He explains to them he has written a positive integer on each hat, and that one of the numbers is the sum of the other two. Each logician can see only the numbers on the other two hats. A prize is offered to the first person able to be certain of the number on his own hat. The wizard starts questioning the logicians in order, starting over again if none of them can be certain of his number. There is no guessing. Each logician must answer: "My number is ___" or "I don't know." [1] Can any of the logicians win the prize? [2] If so, which one? [3] How many rounds of questions will it take? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 2, 2008 Report Share Posted April 2, 2008 you know your #is prime and if you add the other 2 #s together and its a prime # it might be yours but if its not then you know your # pluss the person with the lowest # should = the highest persons # but if you are the person with the highest # and you add the other two # together you should get your # but to be sertan that your answer is corect you - the lowest # YOU SEE by the highest you see if its a prime # that is most likely your # Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 2, 2008 Report Share Posted April 2, 2008 you know your #is prime and if you add the other 2 #s together and its a prime # it might be yours but if its not then you know your # pluss the person with the lowest # should = the highest persons # but if you are the person with the highest # and you add the other two # together you should get your # but to be sertan that your answer is corect you - the lowest # YOU SEE by the highest you see if its a prime # that is most likely your # ... completely lost me Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 2, 2008 Report Share Posted April 2, 2008 sorry Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 2, 2008 Report Share Posted April 2, 2008 sorry don't be sorry! i'm just saying I'm trying to understand what you mean. Is there another way you could explain it? Or is it pretty much as simple as it gets in your explanation? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 2, 2008 Report Share Posted April 2, 2008 you know you are a prime # when you add a+b together and it its a prime # that might be your # if its not a prime # it cant be your # if thats not your # then subtract a-b (if a is bigger) if the answer to that is prime it might be your # Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 2, 2008 Report Share Posted April 2, 2008 But you don't know if yours is prime, that's not the condition Quote Link to comment Share on other sites More sharing options...
Question
bonanova
A wizard selects three excellent logicians and places hats on their heads.
He explains to them he has written a positive integer on each hat, and
that one of the numbers is the sum of the other two. Each logician can
see only the numbers on the other two hats.
A prize is offered to the first person able to be certain of the number on
his own hat. The wizard starts questioning the logicians in order, starting
over again if none of them can be certain of his number.
There is no guessing.
Each logician must answer: "My number is ___" or "I don't know."
[1] Can any of the logicians win the prize?
[2] If so, which one?
[3] How many rounds of questions will it take?
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