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Sun 4 Jan, 2004 04:35 am
A student fails his Mathematics exam and goes postal. He kidnaps three of his teachers, all well-known mathematicians, and keeps them in captivity.
He puts a hat on the head of each one with a number on it.
He tells his captives, "All of the numbers are positive and none of them is zero. They are whole numbers, and one of them is the sum of the other two. All you have to do is figure out what number your hat has on it . . . or else! Mwuhahahah"
The three numbers are 5, 3, 2. (To simplify explanations we will call the one with '5' A, with '3' B; and with '2' C) None of them knows what is on his own hat but he can see the other two.
Can they do it or are they doomed?
I see no restriction against the professors talking to each other...
any one of them has a 50/50 guess...
Well, if they can talk to one another there is no problem . . . apart from their neighborhood loonie not wanting to be thwarted that easily.
As for guessing, I think we can assume that he meant that 'or else'. He will not accept anything other than three correct answers.
Nope; each of the three has to independently discover the number his hat has.
Mungo
Just sent you what I think it the solution in a PM.
Let these other folks have some fun for a while longer.
If my reasoning is wrong, lemme know.
Nothing wrong with your reasoning Frank, but there are three numbers required.
However, having cracked the toughest bit the rest is mere detail I reckon.
Once the guy with the "5" speaks up -- the other two know their numbers immediately.
Excellent riddle, Mungo.
The other one you submitted was also.
Frank
Are you sure you are reading the script? :-)
They will know that he has discovered his number but if he says what he has found it to be, we have already decided, I think, that this would count as communication and would severely upset the neighborhood loonie.
They are aware that he knows; they do not know what he knows.
If they know he knows -- whether he announces it or not. They know what his number is because they can see it.
So if they know he knows -- and if they know he knows he is a 5 -- they know he figured out he was a five because of what he saw. And since they can see the other non-five -- they can figure out for themselves what their number is.
Frank
"They will know what he has because they can see it".
Well of course they can. :-) I am frequently dumb but rarely THAT dumb!!
BTW; seeing as how this problem has been thoroughly dealt with, there is a new one on my 'coins and dice' page that might, I think, be your kind of thing.
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