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        riddles >> easy >> Three numbers
        
(Message started by: mistysakura on Aug 22^nd, 2003, 12:35am)

Title: Three numbers
Post by mistysakura on Aug 22^nd, 2003, 12:35am

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?

Title: Re: Three numbers
Post by towr on Aug 22^nd, 2003, 1:47am

::[hide]
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
[/hide]::

Title: Re: Three numbers
Post by wowbagger on Aug 22^nd, 2003, 1:54am

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. ;)

Title: Re: Three numbers
Post by Sir Col on Aug 22^nd, 2003, 3:12am

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?