Solve this alphametic, where each of the capital letters in bold represents a different decimal digit from 0 to 9. Each of S and T is nonzero.

√(SEE) = √(THE) + √( TOP)

used the following code to find

sqrt(588)=sqrt(108)+sqrt(192)

and this works because sqrt(588)=14*sqrt(3) sqrt(108)=8*sqrt(3) and sqrt(192)=6*sqrt(3)

CLS 0
FOR s = 1 TO 9
 FOR e = 0 TO 9
  IF e <> s THEN
   FOR t = 1 TO 9
    IF t <> s AND t <> e THEN
     FOR h = 0 TO 9
      IF h <> s AND h <> e AND h <> t THEN
       FOR o = 0 TO 9
        IF o <> s AND o <> e AND o <> t AND o <> h THEN
         FOR p = 0 TO 9
          IF p <> s AND p <> e AND p <> t AND p <> h AND p <> o THEN
           v1 = 100 * s + 11 * e
           v2 = 100 * t + 10 * h + e
           v3 = 100 * t + 10 * o + p
           IF SQR(v1) = SQR(v2) + SQR(v3) THEN
            PRINT v1; v2; v3
           END IF
          END IF
         NEXT p
        END IF
       NEXT o
      END IF
     NEXT h
    END IF
   NEXT t
  END IF
 NEXT e
NEXT s

Posted by Daniel on 2009-05-21 15:58:25