(In reply to re(2): computer exploration -- oh, I see a mistake in my reasoning -- solution (spoiler)
(We don't know what brian's nine equations are.) How to you interpret "while the addends are different (but not necessarily unique across the solution set") in the specs? Clearly this cannot mean only that the addends on any given equation are all different: this would be necessary to fit the alphametics criterion (no two digits are represented by the same letter in the same equation). I see all your totals are anagrams of 1113 or 1137, but I don't see any restrictions on that, since all two-digits from either are primes.
(Edit) I also see that the text refers to "the total" perhaps intending that all the equations had the same total. But then he says "some of the totals are replicated." I wish those who write these puzzles were more precise.
Edited on October 7, 2010, 4:43 pm
Edited on October 7, 2010, 4:47 pm