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        riddles >> hard >> Tom's house
        
(Message started by: Moti on Nov 25^th, 2002, 8:25am)

Title: Tom's house
Post by Moti on Nov 25^th, 2002, 8:25am

John is trying to locate tom's house.
but all he know is that tom lives on a street where the houses are numbered 8-100.
so John asks is the house number bigger than 50?
and Tom answers but lies.
Then John asks if the number is a multiplication of 4
and Tom answers and lies again.
Then John asks, does the number have a square root
that is a whole number?
This time Tom answers and tells the truth.
Finally he asks tom if the first digit is 3 and tom answers
but we don't know if it's true or not.
Then John tells him the number and he's of course mistaken.

What number is Tom's house?

??? ??? ???

Title: Re: Tom's house
Post by towr on Nov 25^th, 2002, 8:42am

I think we'll have to assume that there is only one answer John can give when he assumes the answers he is given are true..
So once we know what John has deduced we know which answers where right and can get the real answer..

And now to do it.. (hmmm..)

Title: Re: Tom's house
Post by towr on Nov 25^th, 2002, 9:02am

There seem to be 4 answers John can give: [hide]16, 32, 36 and 81[/hide]
If John needed all questions to determine an answer we can drop the last one. But in that case we also know that[hide] the house number is larger than 50, since only if John mistakenly thinks it is under 50 will he need to ask if it starts with a 3.
Also, the real answer isn't a multiplication of 4, since all of Johns possible answers are, and he was lied to.[/hide]
So the answer must be: [hide]81, the only square not divisible by 4 above 50 and smaller or equal to 100 [/hide]

//Edited by Icarus to use hide tags instead of color to hide the solution

Title: Re: Tom's house
Post by Moti on Nov 25^th, 2002, 11:12am

Bravo!!! ;D ;D ;D