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 9 distinct digits in 3 products (Posted on 2013-01-23)
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 No Rating

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 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  856109           3  6  9       327  654  981123           4  5  6       492  615  738129           1  3  5       129  387  645192           1  2  3       192  384  576219           1  2  3       219  438  657273           1  2  3       273  546  819327           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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