twosummers
Loc: Melbourne Australia or Lincolnshire England
I finally got there! - 381654729 works! It still took me several hours by just trying all "possible" combinations as I stated in the OP. My breakthrough came by recording my "fails" to avoid trying the same combination again. I'm now wondering if there is more than one solution? Well done everyone for having a go!
twosummers wrote:
.... I'm now wondering if there is more than one solution? ....
Nope. There's just one answer. I did write software to verify.
twosummers
Loc: Melbourne Australia or Lincolnshire England
aflundi wrote:
Nope. There's just one answer. I did write software to verify.
Phew! thanks for that aflundi - I can get on with my difference triangle puzzle.......
aflundi wrote:
I think that fails at the 7th digit and 147258369 fails at the 8th . How about 381654729 ?
Yes, you are correct Aflundi. I copied the wrong line on my list of numbers. Good catch.
Daryl
steve33 wrote:
How about this?
129654783
In casting out the 9s, you eliminate all pairs having a total of 9, regardless of their place in the number, and any single digit 9. If all are removed, then the number is divisible by 9. Thus, you cast out (1,8), (2,7), (3,6), (4,5) and 9. Applying that to any 9-digit number that includes all of the digits 1-9 and all will be cast out; therefore, all are divisible by 9. You can probably find the proof of this in even the most elementary book on Number Theory or Discrete Mathematics.
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