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Re: [Hardest Maths Statement Puzzle] Toughest Math Statement Question

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88888 Dihedral wrote:
)> > > divya bisht wrote:
)> > >>
)> > >> Toughest Math Statement Question
)> > >> (Source : http://hardest-puzzle.blogspot.com/2011/12/toughest-math-statement-question.html
)> > >> )
)> > >>
)> > >> I am thinking of a 6-digit number. The sum of the digits is 43.
)> > >>
)> > >> And only two of the following three statements about the number are
)> > >> true:
)> > >>
)> > >> (1) it's a square number,
)> > >> (2) it's a cube number, and
)> > >> (3) the number is under 500000.
) Looking for an integer number rasied to a power of 6  that fits all
)
) conditions in the range should be easy even without writing a program.

No because only two of the three conditions are true.  One is false.
If contition 3 were false, then the number would be both a square and
a cube, and it would be above 500000.  There is exactly one sixth power
between 500000 and 999999, which is 531441, and that does not sum to 43.

So we're looking for a number that's either a cube or a square (but not
 both) between 100000 and 499999.

As a matter of fact, the powers of 6 below 500000 don't sum to 43 either,
so the 'but not both' check is optional, and we can simple scan all squares
and all cubes for the one that has a digit sum of 43:

 for (int s = 317; s < 708; s++)
   if (digit_sum(s*s) == 43)
     printf("%d\n", s*s);
 for (int c = 47; c < 80; c++)
   if (digit_sum(c*c*c) == 43)
     printf("%d\n", c*c*c);

(The function digit_sum should be self-evident.)


SaSW, Willem
-- 
Disclaimer: I am in no way responsible for any of the statements
            made in the above text. For all I know I might be
            drugged or something..
            No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT

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Re: [Hardest Maths Statement Puzzle] Toughest Math Statement Question pete <pfiland@mindspring.com> - 2012-01-07 22:03 -0500
  Re: [Hardest Maths Statement Puzzle] Toughest Math Statement Question Tim Rentsch <txr@alumni.caltech.edu> - 2012-01-26 10:11 -0800
    Re: [Hardest Maths Statement Puzzle] Toughest Math Statement Question pete <pfiland@mindspring.com> - 2012-01-27 17:06 -0500
    Re: [Hardest Maths Statement Puzzle] Toughest Math Statement Question pete <pfiland@mindspring.com> - 2012-01-27 18:30 -0500
      Re: [Hardest Maths Statement Puzzle] Toughest Math Statement Question 88888 Dihedral <dihedral88888@googlemail.com> - 2012-01-31 06:19 -0800
        Re: [Hardest Maths Statement Puzzle] Toughest Math Statement Question Willem <willem@toad.stack.nl> - 2012-03-08 22:26 +0000
      Re: [Hardest Maths Statement Puzzle] Toughest Math Statement Question Tim Rentsch <txr@alumni.caltech.edu> - 2012-01-31 22:28 -0800
        Re: [Hardest Maths Statement Puzzle] Toughest Math Statement Question pete <pfiland@mindspring.com> - 2012-02-01 18:47 -0500
          Re: [Hardest Maths Statement Puzzle] Toughest Math Statement Question Tim Rentsch <txr@alumni.caltech.edu> - 2012-03-08 12:24 -0800

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