(The system refused my post. I assume it was because of its length. So I am posting in parts)The number must meet the following constraints:

1) the fifth digit must be 5

2)the even digits mus be even, and
2a) the fourth and eigth digits must be 2 and 6 in some order, so
2b) the second and sixth digits must be 4 and 8 in some order, and
2c) the first, third, seventh and ninth must be 1,3,7and 9 in some order

3) [This is a consequence of the original constraints that the first 3, 6, and 9 digits are divisible by the specified number of digits] Breaking up the number into three three-digit numbers, the three numbers must each be divisble by 3.

Consider the middle number (digits 4,5,6) By constraint 2, it must be 254, 258, 654, or 658, but by constraint 3 it cannot be 254 or 658. Furthermore, once digits 4 and six are decided, digits 2 and eight are determined. So the number looks like either this: x4x258x6x or this: x8x654x2x

Posted by TomM on 2002-06-07 14:53:20