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One equation with nine unknowns! (2) (Posted on 2012-12-05) Difficulty: 2 of 5
Each of the letters should be replaced by a different base ten digit from 1 to 9 to satisfy this alphanumeric equation:
  A          D        G
------  +  ------ + ------ = 1, with A > D > G, B > C and, E > F   
 B*C        E*F      HI
Can you solve it, knowing that if I told you whether HIG is a perfect square or not, you would be able to tell me all the other letters?

Note: Each of HI and HIG represents the concatenation of the digits.

No Solution Yet Submitted by K Sengupta    
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Solution computer solution | Comment 1 of 3

   10   V$="123456789":H$=V$
   15   repeat
   20      gosub *Permute(&V$)
   30      A=val(mid(V$,1,1))
   40      D=val(mid(V$,4,1))
   50      G=val(mid(V$,7,1))
   60      if A>D and D>G then
   70        :B=val(mid(V$,2,1))
   80        :C=val(mid(V$,3,1))
   90        :E=val(mid(V$,5,1))
  100        :F=val(mid(V$,6,1))
  110        :H=val(mid(V$,8,1))
  120        :I=val(mid(V$,9,1))
  130        :if B>C and E>F then
  140           :Hi=10*H+I
  150           :Hig=10*Hi+G
  160           :Sr=sqrt(Hig)
  170           :if A//(B*C)+D//(E*F)+G//(Hi)=1 then
  180               :print A;B;C;D;E;F;G;H;I,Hig;Sr
  535   until V$=H$
  540   end
  800 

finds the following all satisfy the equation:

 a  b  c  d  e  f  g  h  i       hig     sqrt(hig)
 5  6  1  4  9  8  3  2  7       273  16.5227116418583060617
 6  8  1  5  9  4  3  2  7       273  16.5227116418583060617
 8  4  3  6  9  7  5  2  1       215  14.662878298615180145
 8  6  4  5  9  1  3  2  7       273  16.5227116418583060617
 9  6  2  5  7  3  1  8  4       841  29.0
 9  7  3  8  6  4  5  2  1       215  14.662878298615180145

 
so the penultimate line is the answer, where hig = 841 = 29^2, the only perfect square value for hig.


  Posted by Charlie on 2012-12-05 12:22:19
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