The alphametic
SWAN+MEDIC=IDIOM
yields 8 solutions in base 10, but only one of them may help you answer the following question:

What are the latitude and the longitude of:
7248901,389601981?

The computer program below produced the following table.  I have however added in the co-ordinates for Madison, Wisconson which I derived from Google Earth.
While the actual variables of the "For..Next" loops could not be employed they were used as pointers to store constants of the same name within a string array.  
These string values were then concatenated for the alpha output.

 9326  75481  84807
MADISOC, WISNOCSIC

 5326  79481  84807
MADIEOC, WIENOCEIC

 9321  75486  84807
MADISON, WISCONSIN  (43*4'N, 89*24'W)

 5321  79486  84807
MADIEON, WIECONEIN

 9438  52167  61605
CEWNSOD, ANSIODSND

 2438  59167  61605
CSWNEOD, ANEIODEND

 9437  52168  61605
NEWCSOD, ACSIODSCD

 2437  59168  61605
NSWCEOD, ACEIODECD




OPEN "c:\qb64\work\idiom.txt" FOR OUTPUT AS #1

DIM x(10) AS STRING
FOR a = 0 TO 9
 IF used(a) = 0 THEN
  used(a) = 1: x(a) = "A"
  FOR c = 0 TO 9
   IF used(c) = 0 THEN
    used(c) = 1: x(c) = "C"
    FOR d = 0 TO 9
     IF used(d) = 0 THEN
      used(d) = 1: x(d) = "D"
      FOR e = 0 TO 9
       IF used(e) = 0 THEN
        used(e) = 1: x(e) = "E"
        FOR i = 1 TO 9
         IF used(i) = 0 THEN
          used(i) = 1: x(i) = "I"
          FOR m = 1 TO 9
           IF used(m) = 0 THEN
            used(m) = 1: x(m) = "M"
            FOR n = 0 TO 9
             IF used(n) = 0 THEN
              used(n) = 1: x(n) = "N"
              FOR o = 0 TO 9
               IF used(o) = 0 THEN
                used(o) = 1: x(o) = "O"
                FOR s = 1 TO 9
                 IF used(s) = 0 THEN
                  used(s) = 1: x(s) = "S"
                  FOR w = 0 TO 9
                   IF used(w) = 0 THEN
                    used(w) = 1: x(w) = "W"
                    swan = s * 1000 + w * 100 + a * 10 + n
                    medic = m * 10000 + e * 1000 + d * 100 + i * 10 + c
                    idiom = i * 10000 + d * 1000 + i * 100 + o * 10 + m
                    pl1$ = "": pl2$ = ""
                    IF swan + medic = idiom THEN
                     pl1$ = x(7) + x(2) + x(4) + x(8) + x(9) + x(0) + x(1)
                     pl2$ = x(3) + x(8) + x(9) + x(6) + x(0) + x(1) + x(9) + x(8) + x(1)

                     PRINT swan; medic; idiom
                     PRINT pl1$; ", "; pl2$
                     '   PRINT

                     PRINT #1, swan; medic; idiom
                     PRINT #1, pl1$; ", "; pl2$

                     PRINT #1,


                    END IF


                    used(w) = 0
                   END IF
                  NEXT
                  used(s) = 0
                 END IF
                NEXT
                used(o) = 0
               END IF
              NEXT
              used(n) = 0
             END IF
            NEXT
            used(m) = 0
           END IF
          NEXT
          used(i) = 0
         END IF
        NEXT
        used(e) = 0
       END IF
      NEXT
      used(d) = 0
     END IF
    NEXT
    used(c) = 0
   END IF
  NEXT
  used(a) = 0
 END IF
NEXT

CLOSE 1

Posted by brianjn on 2013-10-16 21:47:56