What 6-digit number ABCDEF is divisible evenly by GHI ?

Rem 1: The letters represent 9 distinct non-zero digits.
Rem 2: The digits A,B,C,D,E are in increasing order.
Rem 3: There are several solutions.

 
Within the queue I mentioned to Ady that the original proposal had vast solutions.  I put Ady the further possibility of changing his problem to offer just one solution*.

Dej Mar and Charlie offer a similar table as what follows.  My Computer listing is less efficient than Charlie's although I think I may have limited the scope of the FOR .. NEXT LOOPs in a later trial but did not save them.


tmpt   num   dvr  quo
1  125673  489  257
 2  136782  459  298
 3  147896  532  278
 4  156784  239  656
 5  156792  834  188
 6  156894  237  662
 7  246789  153  1613    *
 8  256794  381  674
 9  257891  463  557
 10  345681  279  1239
 11  345897  621  557
 12  567891  243  2337
 13  567892  134  4238


tmpt = 1
OPEN "c:\qb64\work\once.txt" FOR OUTPUT AS #1

FOR a = 1 TO 9
IF used(a) = 0 THEN
used(a) = 1
FOR b = 1 TO 9
IF used(b) = 0 THEN
used(b) = 1
FOR c = 1 TO 9
IF used(c) = 0 THEN
used(c) = 1
FOR d = 1 TO 9
IF used(d) = 0 THEN
used(d) = 1
FOR e = 1 TO 9
IF used(e) = 0 THEN
used(e) = 1
FOR f = 1 TO 9
IF used(f) = 0 THEN
used(f) = 1
FOR g = 1 TO 9
IF used(g) = 0 THEN
used(g) = 1
FOR h = 1 TO 9
IF used(h) = 0 THEN
used(h) = 1
FOR i = 1 TO 9
IF used(i) = 0 THEN
used(i) = 1
num = a * 10 ^ 5 + b * 10 ^ 4 + c * 10 ^ 3 + d * 10 ^ 2 + e * 10 + f
dvr = g * 100 + h * 10 + i
quo = num / dvr
LOCATE 1, 1: PRINT a; b; c; d; e; f; g; h; i, num; dvr; quo
IF quo = INT(quo) THEN
LOCATE 3, 1: PRINT tmpt, num; dvr; quo
PRINT #1, tmpt; num; dvr; quo
tmpt = tmpt + 1
END IF

used(i) = 0
END IF
NEXT
used(h) = 0
END IF
NEXT
used(g) = 0
END IF
NEXT
used(f) = 0
END IF
NEXT
used(e) = 0
END IF
NEXT
used(d) = 0
END IF
NEXT
used(c) = 0
END IF
NEXT
used(b) = 0
END IF
NEXT
used(a) = 0
END IF
NEXT

CLOSE 1

Posted by brianjn on 2012-06-09 21:27:38