Determine all possible values of a 6digit positive integer N having 6 different digits from 0 to 9, with the first digit being nonzero, such that:
(i) Either, the digits at the even positions are even and the digits at the odd positions are odd – or, the digits at the even positions are odd and the digits at the odd positions are even. Zero is regarded as an even digit.
(ii) The absolute difference between two adjacent digits is always greater than one.
(iii) The 2digit number formed by the first and second digit as well as the 2digit number formed by the third and fourth digit is divisible by the 2digit number formed by the fifth and sixth digit.
DEFDBL AZ
FOR a = 1 TO 9
used(a) = 1
FOR b = 0 TO 9
IF used(b) = 0 AND (a + b) MOD 2 = 1 AND ABS(a  b) > 1 THEN
used(b) = 1
FOR c = 0 TO 9
IF used(c) = 0 AND (c + b) MOD 2 = 1 AND ABS(b  c) > 1 THEN
used(c) = 1
FOR d = 0 TO 9
IF used(d) = 0 AND (c + d) MOD 2 = 1 AND ABS(c  d) > 1 THEN
used(d) = 1
FOR e = 0 TO 9
IF used(e) = 0 AND (d + e) MOD 2 = 1 AND ABS(d  e) > 1 THEN
used(e) = 1
FOR f = 0 TO 9
IF used(f) = 0 AND (e + f) MOD 2 = 1 AND ABS(e  f) > 1 THEN
used(f) = 1
ab = 10 * a + b
cd = 10 * c + d
ef = 10 * e + f
IF ab MOD ef = 0 AND cd MOD ef = 0 THEN
PRINT a; b; c; d; e; f
END IF
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
NEXT
finds the previously given
4 9 6 3 0 7
6 9 2 7 0 3
8 1 6 3 0 9
8 1 6 9 0 3
9 0 3 6 1 8
I note that KS did not specifically forbid leading zeros from the 2digit numbers (whereas he had from the 6digit number), so there could be a difference of opinion about the validity of the first four solutions.

Posted by Charlie
on 20100101 14:01:25 