As noted by others, if the answer includes a 5 it must end in 5, which would preclude all of 2, 4, 6 and 8.

However you may also spot that the digits 12346789 do not have a sum divisible by 3, so we must lose a 1, 4 or 7 to avoid losing all of 3, 6 and 9. Of those, only 4 leaves us a digit sum divisible by 9, so if a 7-digit solution is possible it must consist of 1236789.

The gcd of those digits is 7*8*9 = 504, so we can start at 504 * int(9876321/504), and work down in steps of 504 until we find a multiple that consists of the right set of digits; as it turns out, just 17 such steps take us to the answer, and we could reasonably do that much by hand (though I didn't :).

Hugo

In reply to Re: Puzzle: What is the largest integer whose digits are all different (and do not include 0) that is divisible by each of its individual digits? by hv
in thread Puzzle: What is the largest integer whose digits are all different (and do not include 0) that is divisible by each of its individual digits? by tphyahoo

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