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 [SOLVED] mathemagics

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peyman
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PostSubject: [SOLVED] mathemagics   Thu Nov 19, 2009 12:18 am

This problem should be easy for you guys, but here we go:

In a parlour game, the 'magician' asks one of the participants to think of a three-digit number abc. then the magician asks the participant to add the five numbers acb, bac, bca, cab, and cba, and reveal their sum. Suppose the sum was 3194. What was abc? cat affraid
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Bruno
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PostSubject: Re: [SOLVED] mathemagics   Thu Nov 19, 2009 4:28 am

358 flower
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peyman
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PostSubject: Re: [SOLVED] mathemagics   Thu Nov 19, 2009 9:43 am

by trial and error or systematic?
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Bruno
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PostSubject: Re: [SOLVED] mathemagics   Thu Nov 19, 2009 12:04 pm

half/half... I tried less than 20, not that bad!

Do you have a 100% systematic way?
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peyman
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PostSubject: Re: [SOLVED] mathemagics   Thu Nov 19, 2009 12:18 pm

Bruno wrote:
half/half... I tried less than 20, not that bad!

Do you have a 100% systematic way?
not 100% systematic but I only tried 2.
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PostSubject: Re: [SOLVED] mathemagics   Thu Nov 19, 2009 12:57 pm

I was quite drunk, so 20 isn't that bad drunken. When you're drunk, there is nothing more systematic than trial and error. I think it took me 20 trials to unlock the door of my apartment! Razz
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peyman
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PostSubject: Re: [SOLVED] mathemagics   Thu Nov 19, 2009 7:15 pm

trial and error is completely acceptable when you are drunk, afterall it is very dangerous to drink and derive! geek
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PostSubject: Re: [SOLVED] mathemagics   Thu Nov 19, 2009 10:41 pm

ta dam tssshhh! cheers
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PostSubject: Re: [SOLVED] mathemagics   Fri Nov 20, 2009 2:32 pm

So what's your solution, Peyman?
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Mohammad
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PostSubject: Re: [SOLVED] mathemagics   Sat Nov 21, 2009 9:12 pm

I could find the number just by three trials hehe, since
abc+ 3194= 222(a+b+c) we get 3194 \ge 222(a+b+c) \le 2.(3194) or 14 \ge (a+b+c)\le 28
bounce
It is an embarrassing solution pls upload the real solution Embarassed
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peyman
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PostSubject: Re: [SOLVED] mathemagics   Sun Nov 22, 2009 9:57 pm

ok here's my embarrassing solution Embarassed :

222(a+b+c)=3194+abc =>

abc =-3194 =136 (mod 222)

so I tried abc=136, and then abc=136+222=358. Here a miracle happened affraid : for the first time in my life I got lucky and 358 worked.
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PostSubject: Re: [SOLVED] mathemagics   Sun Nov 22, 2009 10:01 pm

of course had I been less lucky and perhaps more drunk (like some other people we don't mention Smile ) it would've taken me more tries.
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Mohammad
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PostSubject: Re: [SOLVED] mathemagics   Sun Nov 22, 2009 10:09 pm

Ok, cool down. Poor Bruno receives funny critics these days! Very Happy
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peyman
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PostSubject: Re: [SOLVED] mathemagics   Sun Nov 22, 2009 10:27 pm

I'm sure he's cool with it. (watch him ban both of us now from the forum Laughing )
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PostSubject: Re: [SOLVED] mathemagics   Mon Nov 23, 2009 2:59 am

Just a temporary ban, 24 hours jocolor

I'm coming back from a karaoke bar, I sang "Barbie Girl" silent . (I was singing Ken's part, fortunately).

drunken
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