Substitute each of the capital letters in bold by a different base ten digit from 0 to 9 to satisfy this alphametic equation. Neither P nor O can be zero.

PANE = [OUTSHOUT/ PIANO], where the remainder obtained upon dividing OUTSHOUT by PIANO is less than 500.

Note: [x] denotes the greatest integer ≤ x.

(In reply to re: Missed Solution? by Charlie)

&^#$@!!!!

Thanks again Charlie.

I missed building that comparison into my sheet!!

I even went to the point of rewriting Daniel's program (with a few adjustments) so as to use your "used(x)" construction which naturally found only one solution.

That listing appears below:

OPEN "piano2.txt" FOR OUTPUT AS #1

CLS 0
FOR p = 1 TO 9
IF used(p) = 0 THEN
   used(p) = 1
 FOR o = 1 TO 9
  IF used(o) = 0 THEN
     used(o) = 1
   FOR n = 0 TO 9
    IF used(n) = 0 THEN
       used(n) = 1
     FOR e = 0 TO 9
      IF used(e) = 0 THEN
         used(e) = 1
       FOR h = 0 TO 9
        IF used(h) = 0 THEN
           used(h) = 1
         FOR u = 0 TO 9
          IF used(u) = 0 THEN
             used(u) = 1
           FOR t = 0 TO 9
            IF used(t) = 0 THEN
               used(t) = 1
             FOR s = 0 TO 9
              IF used(s) = 0 THEN
                 used(s) = 1
               FOR a = 0 TO 9
                IF used(a) = 0 THEN
                   used(a) = 1
                 FOR i = 0 TO 9
                  IF used(i) = 0 THEN
                     used(i) = 1
                   v1 = 1000 * p + 100 * a + 10 * n + e
                   v2 = (10 ^ 7) * o + (10 ^ 6) * u + (10 ^ 5) * t + (10 ^ 4) * s + (10 ^ 3) * h + (10 ^ 2) * o + 10 * u + t
                   v3 = o + 10 * n + 100 * a + 1000 * i + 10000 * p
                   fl = INT(v2 / v3)
                   rm = v2 - fl * v3
                   IF fl = v1 AND rm <= 500 THEN
                    PRINT v1, v2, v3, rm
                    PRINT p; a; n; e; o; u; t; s; h; i
                    PRINT #1, p; a; n; e; o; u; t; s; h; i
                    PRINT #1, v1; v2, v3, rm
                   END IF
                 
                 used(i) = 0
                 END IF
                 NEXT
               
               used(a) = 0
               END IF
               NEXT
             
             used(s) = 0
             END IF
             NEXT
           
           
           used(t) = 0
           END IF
           NEXT
         
         used(u) = 0
         END IF
         NEXT
       
       used(h) = 0
       END IF
       NEXT
     
     used(e) = 0
     END IF
     NEXT
   
   used(n) = 0
   END IF
   NEXT
 
 used(o) = 0
 END IF
 NEXT
 
used(p) = 0
END IF
NEXT

CLOSE 1

Posted by brianjn on 2009-08-13 02:45:35