SOLUTION: I need HELP solving this problem PLEASE. (1)a door code is made up of six unique digits the last digit is eight. (2)odd and even digits alternate zero is even. (3)the difference of

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Question 151580: I need HELP solving this problem PLEASE. (1)a door code is made up of six unique digits the last digit is eight. (2)odd and even digits alternate zero is even. (3)the difference of adjacent digits is always larger than one. (4)the first two digits read as one number as well as the middle digits read as one number are multiples of the last two digits read as one
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
The next to last digit must be odd, because odd and even digits
must alternate and the last digit is 8.

Therefore the last two digits must either be 18, 38, 58, 78, or 98

But since the first two digits and the middle two digits
are unique multiples of the last two digits, the last two digits 
must have at least two different 2-digit multiples.

38 has only one 2-digit multiple, 76. So it won't do.  58, 78, 
and 98 have no 2-digit multiples.  So they won't do.

So the only possibility for the last two digits is 18, because 18 has
four 2-digit multiples, 36, 54, 72, and 90 

So we have:

_ _ _ _ 1 8

The first two digits and the middle two digits must both be
multiples of 18.  We cannot use 54 because its digits differ
by 1, so they must be two of these:  36, 72 or 90

We cannot put 72 or 90 in the middle before the 18, because the
second digit of either one and the first digit of 18 would only 
differ by 1 in either case.

Therefore the middle two digits can only be 36.

So we have

_ _ 3 6 1 8

So that leaves 72 or 90 for the first two digits.

We cannot put 72 there for its second digit 2
would differ from the third digit 3, by only 1.

That leaves only 90 for the first two digits.

So the answer is

903618 

Edwin

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