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 One equation with nine unknowns! (2) (Posted on 2012-12-05)
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 No Rating

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 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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