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Piano and Potent Pane (Posted on 2009-08-12) Difficulty: 2 of 5
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.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
basic solution | Comment 1 of 6

using Qbasic I found
PANE=1670
OUTSHOUT=32854328
PIANO=19673
and this gives a remainder of 418

My Qbasic program follows

CLS 0
FOR p = 1 TO 9
 FOR a = 0 TO 9
  IF a <> p THEN
   FOR n = 0 TO 9
    IF n <> p AND n <> a THEN
     FOR e = 0 TO 9
      IF e <> p AND e <> a AND e <> n THEN
       v1# = 1000 * p + 100 * a + 10 * n + e
       FOR o = 1 TO 9
        IF o <> p AND o <> a AND o <> n AND o <> e THEN
         FOR u = 0 TO 9
          IF u <> p AND u <> a AND u <> n AND u <> e AND u <> o THEN
           FOR t = 0 TO 9
            IF t <> p AND t <> a AND t <> n AND t <> e AND t <> o AND t <> u THEN
             FOR s = 0 TO 9
              IF s <> p AND s <> a AND s <> n AND s <> e AND s <> o AND s <> u AND s <> t THEN
               FOR h = 0 TO 9
                IF h <> p AND h <> a AND h <> n AND h <> e AND h <> o AND h <> u AND h <> t AND h <> s THEN
                 v2# = (10 ^ 7) * o + (10 ^ 6) * u + (10 ^ 5) * t + (10 ^ 4) * s + (10 ^ 3) * h + (10 ^ 2) * o + 10 * u + t
                 FOR i = 0 TO 9
                  IF i <> p AND i <> a AND i <> n AND i <> e AND i <> o AND i <> u AND i <> t AND i <> s AND i <> h THEN
                   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#
                   END IF
                  END IF
                 NEXT i
                END IF
               NEXT h
              END IF
             NEXT s
            END IF
           NEXT t
          END IF
         NEXT u
        END IF
       NEXT o
      END IF
     NEXT e
    END IF
   NEXT n
  END IF
 NEXT a
NEXT p


 


  Posted by Daniel on 2009-08-12 11:40:33
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