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.

(In reply to re: computer solution by Jer)

The D > G was specified in the puzzle.

Indeed allowing G > D does produce other solutions to the equation, but the specification of perfect square or not would not then eliminate the ambiguity, as there would be 3 HIGs that are perfect squares:

 5  6  1  4  9  8  3  2  7       273  16.5227116418583060617
 5  7  2  4  8  1  9  6  3       639  25.2784493195290758918
 5  7  4  3  6  1  9  2  8       289  17.0
 5  8  3  4  6  1  9  7  2       729  27.0
 5  9  1  4  8  2  7  3  6       367  19.1572440606680166603
 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  7  3  9  2  1       219  14.798648586948742057
 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
 9  7  4  3  6  1  5  2  8       285  16.8819430161341321831
 9  8  3  2  4  1  7  5  6       567  23.8117617995813153145

Posted by Charlie on 2012-12-05 13:33:02