DiMono
Level: Smitemaster
Rank Points: 1162
Registered: 09132003
IP: Logged

Re: Puzzle "tag" (+1)
381654729
Edit: Gah, you and your fast fingers got in there ahead of me. I may as well explain why it works that way though.
All the even digits must be even, and the middle digit must be a 5. It doesn't matter what the last digit is, because the sum of 19 is 45, and any number whose digits add to a number divisible 9 is itself divisible by 9, so that part is automatic.
Similarly, any digit whose digits add to a number divisible by 3 is divisible by 3. This means the first set of 3 digits must be divisible by 3, as must the second set of 3 digits. The only number combinations that can be used for the middle are 456, 654, 258, and 852.
Testing the third and fourth number sets is easy, because there are only 4 numbers that can be before them: 147, 741, 369, and 963. Any other combination would invalidate a previous restriction. None of the 8 combinations allow an 8 digit number divisible by 8, so we're working with 456 and 654. Our options for the first 3 digits are as follows:
123, 321, 129, 921, 723, 327, 729, 927
183, 381, 189, 981, 783, 387, 789, 987
It happens that for all those combinations, the fourth digit must be a 6 instead of a 4, so our number is going to look like OEO654OEO. Now it's just trial and error, and 381654729 is the only solution that works. And that's how we got to the number we got to.
[Edited by DiMono on 08062004 at 06:50 PM GMT]
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