Solve this alphametic, where each of the capital letters in bold denotes a different decimal digit from 0 to 9. None of the numbers can contain any leading zero.

³√(HOW)+ ³√(AND) = ³√(WHEN)

The program below finds two solutions!
  HOW        192           736
  AND         375           952
WHEN       2187         6715

Using Excel to calculate the sum of the roots of HOW and AND and comparing the root of WHEN there is no difference in the precision of the first instance.  In the second instance the sum is:
18.866084....  while the root of the WHEN is 18.866094...

For the reason of precision I'd have to disregard the second result.

Back to the program.  If the two lines mentioned in the middle of the program are comment out I get no result!  Why is this?  Is the precision of QuickBASIC greater than Excel?
----------------------------------------------------------------------------
This is based on an algorithm posted by Charlie at A Great Time Waster.
----------------------------------------------------------------------------
DIM SHARED used(10)

CLS

OPEN "CUBES.TXT" FOR OUTPUT AS #1

FOR h = 1 TO 9
 IF used(h) = 0 THEN
    used(h) = 1

FOR a = 1 TO 9
 IF used(a) = 0 THEN
    used(a) = 1

FOR w = 1 TO 9
 IF used(w) = 0 THEN
    used(w) = 1

FOR e = 0 TO 9
 IF used(e) = 0 THEN
    used(e) = 1

FOR d = 0 TO 9
 IF used(d) = 0 THEN
    used(d) = 1

FOR n = 0 TO 9
 IF used(n) = 0 THEN
    used(n) = 1

FOR o = 0 TO 9
 IF used(o) = 0 THEN
    used(o) = 1

x = h * 100 + o * 10 + w
y = a * 100 + n * 10 + d
z = w * 1000 + h * 100 + e * 10 + n

j = x ^ (1 / 3)
k = y ^ (1 / 3)
l = z ^ (1 / 3)

REM ------------------------------------

 q = j + k    ' REM the next two lines and run.

 q = VAL(LTRIM$(LEFT$((STR$(q)), 20)))

 l = VAL(LTRIM$(LEFT$((STR$(l)), 20)))

REM ------------------------------------


IF (l = q) THEN

PRINT #1, x; y; z; "   "; h; a; w; e; d; n; o
PRINT x; y; z; "   "; h; a; w; e; d; n; o
END IF

used(o) = 0
END IF
NEXT
used(n) = 0
END IF
NEXT
used(d) = 0
END IF
NEXT
used(e) = 0
END IF
NEXT
used(w) = 0
END IF
NEXT
used(a) = 0
END IF
NEXT
used(h) = 0
END IF
NEXT

CLOSE 1

Edited on July 30, 2009, 2:02 am

Posted by brianjn on 2009-07-30 01:44:40