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Topic: Three numbers (Read 431 times) |
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mistysakura
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Three numbers
« on: Aug 22nd, 2003, 12:35am » |
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A nice and easy riddle I heard the other day. It seems too easy for the 'easy' forum, but obviuosly there is nowhere else to put it.
There are three children, and each of them is told a natural number. The children do not know the other children's numbers, and they are not allowed to tell the others what number they have. Their only piece of information is that the three numbers add up to 14.
The first child says, " I know you two have different numbers, but I don't know what they are."
The second child then says, "I knew all along that all three of us had different numbers, but I didn't know, and still don't know, what your numbers are."
The thire child then realises what the three numbers are.
so, what are the three numbers?
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| « Last Edit: Aug 22nd, 2003, 12:36am by mistysakura » |
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towr
wu::riddles Moderator
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Re: Three numbers
« Reply #1 on: Aug 22nd, 2003, 1:47am » |
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If 0 is excluded from the natural numbers:
the first child has an odd number, that way the other two numbers can't be the same and add up to 14 at the same time
the second child also has an odd number and it's 7 or higher so it can't be the same as one of the other two, nor can the other two be the same as eachother.
the third child now has enough information to solve the puzzle knowing his number
1 11 2 [e]there need to be 2 or more options for child 2 left[/e]
1 9 4
3 9 2
1 7 6
3 7 4
5 7 2
so it has to be 1 7 6
If we include 0 in the natural numbers we get a slightly different choice, since child 2 needs a 9 or higher (else one and two may both have 7)
1 13 0
1 11 2
3 11 0
1 9 4
3 9 2
5 9 0
so in this case it's 1 9 4
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| « Last Edit: Aug 22nd, 2003, 1:50am by towr » |
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wowbagger
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Re: Three numbers
« Reply #2 on: Aug 22nd, 2003, 1:54am » |
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This time you beat me by a few minutes, towr. 
I'm glad I realized in time so I didn't unnecessarily write all that myself. 
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Sir Col
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Re: Three numbers
« Reply #3 on: Aug 22nd, 2003, 3:12am » |
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How can it be easier than easy, mistysakura? It's a lovely, and relatively challenging, puzzle indeed; thanks for sharing it.
Here's an extension...
This time, the three (counting) numbers add up to N.
What is the largest N, such that the 1st child would not know the numbers, but the 2nd child would be able to determine the numbers?
What is the smallest N, such that the 3rd child would not know the numbers?
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