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A couple of observations from number theory to reduce the search space. The number 2003 is congruent to 5 mod 9, and taking sums of base-ten digits reduces them mod 9. If three permutations of digits \$x, \$y, and \$z could solve the puzzle, then:
```(3*(\$x+\$y+\$z) % 9) == 5
[download]```
But 3 has no inverse mod 9 because of the common factor, so it's impossible with 3 permutations.
```if (4*(\$x+\$y+\$z) % 9) == 5  then (\$x+\$y+\$z) % 9 = 8
if (5*(\$x+\$y+\$z) % 9) == 5  then  (\$x+\$y+\$z) % 9 = 1
if (7*(\$x+\$y+\$z) % 9) == 5  then  (\$x+\$y+\$z) % 9 = 2
[download]```
6 is impossible because of the common factor. For any given \$x, \$y you can calculate what \$z would have to be (or eliminate it if it's a duplicate of the others). That should cut down your search space by a lot.

In reply to Re: Coming soon: Algorithm::Loops by tall_man
in thread Coming soon: Algorithm::Loops by tye

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