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 Digits 1-7 (Posted on 2009-03-30)
A seven digit positive octal integer X is constituted by arranging the nonzero octal digits 1-7 in some order, so that:
• The octal number formed by the first two digits is divisible by 2.
• The octal number formed by the first three digits is divisible by 3.
• The octal number formed by the first four digits is divisible by 4.
• and, so on up to seven digits...
Determine all possible value(s) that X can assume.

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution | Comment 1 of 6

DECLARE FUNCTION oct2dec# (o\$)
DEFDBL A-Z
DECLARE SUB permute (a\$)
CLS
dig\$ = "1234567"
h\$ = dig\$
DO
IF oct2dec(LEFT\$(dig\$, 2)) MOD 2 = 0 THEN
IF oct2dec(LEFT\$(dig\$, 3)) MOD 3 = 0 THEN
IF oct2dec(LEFT\$(dig\$, 4)) MOD 4 = 0 THEN
IF oct2dec(LEFT\$(dig\$, 5)) MOD 5 = 0 THEN
IF oct2dec(LEFT\$(dig\$, 6)) MOD 6 = 0 THEN
IF oct2dec(LEFT\$(dig\$, 7)) MOD 7 = 0 THEN
PRINT dig\$;
PRINT oct2dec(LEFT\$(dig\$, 2));
PRINT oct2dec(LEFT\$(dig\$, 3));
PRINT oct2dec(LEFT\$(dig\$, 4));
PRINT oct2dec(LEFT\$(dig\$, 5));
PRINT oct2dec(LEFT\$(dig\$, 6));
PRINT oct2dec(LEFT\$(dig\$, 7))
END IF
END IF
END IF
END IF
END IF
END IF

permute dig\$
LOOP UNTIL h\$ = dig\$

FUNCTION oct2dec (o\$)
v = 0
FOR i = 1 TO LEN(o\$)
v = v * 8 + VAL(MID\$(o\$, i, 1))
NEXT
oct2dec = v
END FUNCTION

finds three values:

`3254167 26  213  1708  13665  109326  8746155234761 42  339  2716  21735  173886  13910895674321 46  375  3004  24035  192282  1538257`

where the first column is the octal number, and the remaining columns show the decimal equivalents of the first 2, 3, 4, 5, 6 and 7 digits.

 Posted by Charlie on 2009-03-30 13:47:39
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