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9 distinct digits in 3 products (Posted on 2013-01-23) Difficulty: 3 of 5
A certain 3-digit number, when multiplied
by 3 different digits provides three 3-digit results jointly using all non-zero digits.

What number is it?


Is there only one such a number?.

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solution Comment 2 of 2 |

DEFDBL A-Z
FOR n = 100 TO 999
  FOR a = 1 TO 7
   na = n * a
  FOR b = a + 1 TO 8
   nb = n * b
  FOR c = b + 1 TO 9
   nc = n * c
   chk$ = LTRIM$(STR$(na)) + LTRIM$(STR$(nb)) + LTRIM$(STR$(nc))
   REDIM digchk(9)
   FOR i = 1 TO LEN(chk$)
     digchk(VAL(MID$(chk$, i, 1))) = 1
   NEXT
   good = 1
   FOR i = 1 TO 9
     IF digchk(i) = 0 THEN good = 0
   NEXT
   IF good AND LEN(chk$) = 9 THEN
     PRINT n, a; b; c, na; nb; nc
   END IF
  NEXT
  NEXT
  NEXT
NEXT

finds

107           3  7  8       321  749  856
109           3  6  9       327  654  981
123           4  5  6       492  615  738
129           1  3  5       129  387  645
192           1  2  3       192  384  576
219           1  2  3       219  438  657
273           1  2  3       273  546  819
327           1  2  3       327  654  981
 

123 multiplied by 4, 5 and 6 (the third line) has a certain ring to it; it's the only one in which none of the single digits appear in the original 3-digit number.

Edited on January 23, 2013, 12:43 pm
  Posted by Charlie on 2013-01-23 12:42:01

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